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Department of Number Theory

| Seminars | History of the Department | Research Directions | Main results | Publications |
Staff
Konyagin Sergei Vladimirovich

Doctor Phys.-Math. Sci., Professor, Academician of RAS, Head of Department
office: 520; tel.: +7 (499) 941 01 90; e-mail: konyagin23@gmail.com, konyagin@mi.ras.ru
Principal fields of research: Trigonometric series. Polynomials. Best approximation. Character sums.
Konyagin Sergei Vladimirovich
Frolenkov Dmitrii Andreevich

Candidate Phys.-Math. Sci., Scientific Researcher
office: 509; tel.: +7 (495) 984 81 41 * 36 07; e-mail: frolenkov@mi.ras.ru
Principal fields of research: Analytic number theory. Automorphic functions. Kloosterman sums. $L$-functions. Continued fractions.
Frolenkov Dmitrii Andreevich
Korolev Maxim Aleksandrovich

Doctor Phys.-Math. Sci., Leading Scientific Researcher
office: 526; tel.: +7 (495) 984 81 41 * 37 32; e-mail: korolevma@mi.ras.ru
Principal fields of research: Incomplete Kloosterman sums, argument of Riemann's zeta-function, power residues, the average number of power residues, the problem of Lehmer–Landau.
Korolev Maxim Aleksandrovich
Rezvyakova Irina Sergeevna

Candidate Phys.-Math. Sci., Senior Scientific Researcher
office: 526; tel.: +7 (495) 984 81 41 * 37 32; e-mail: rezvyakova@mi.ras.ru
Principal fields of research: Analytic number theory.
Rezvyakova Irina Sergeevna
Shkredov Il'ya Dmitrievich

Doctor Phys.-Math. Sci., Corresponding Member of RAS, Chief Scientific Researcher
office: 509; tel.: +7 (495) 984 81 41 * 36 07; e-mail: ilya.shkredov@gmail.com, ishkredov@rambler.ru
Personal page: http://www.mi.ras.ru/~ishkredov/
Principal fields of research: Additive combinatorics, number theory, ergodic number theory.
Shkredov Il'ya Dmitrievich

Arkhipov Gennadii Ivanovich (12.12.1945 – 14.03.2013)

Doctor Phys.-Math. Sci.

Principal fields of research: Number theory, mathematical analysis.
Iskovskikh Vasilii Alekseevich (1.07.1939 – 4.01.2009)

Doctor Phys.-Math. Sci., Corresponding Member of RAS

Principal fields of research: Rationality problem, birational rigidity, birational classification.
Karatsuba Anatolii Alekseevich (31.01.1937 – 28.09.2008)

Doctor Phys.-Math. Sci.

Personal page: http://www.mi.ras.ru/~karatsuba
Principal fields of research: Analytic number theory and mathematical cybernetics.
Top
Seminars
Contemporary Problems in Number Theory
Seminar Chairmen: S. V. Konyagin; I. D. Shkredov; Seminar Secretary: D. Frolenkov
Steklov Mathematical Institute, Room 530 (8 Gubkina)
Top
History of the Department

The Department ofNumber Theory was organized in1934. Academician I.M.Vinogradov was the Head of the Department in 19341983. Since1983 Prof.A.A.Karatsuba is the Head of theDepartment.

In 2010 the Department of Number theory was merged with the Department of Algebra. Aleksei N. Parshin, corresponding member of the Russian Academy of Sciences, was appointed the head of the new Department of Algebra and Number theory. In 2016 the Department of Number theory has been re-established as as an independent unit of the institute. Head of the Department is S.V. Konyagin, corresponding member of the Russian Academy of Sciences.

At different times, G. I. Arkhipov, K.K.Mardzhanishvili, A.O.Gelfond, B.I.Segal, L.G.Shnirel'man, N.M.Korobov, L.P.Postnikova, N.V.Kuznetsov, S.A.Stepanov, A.I.Vinogradov, A.G.Postnikov, K.I.Oskolkov, S.M.Voronin, A.I.Pavlov, I.Yu.Fedorov, and M.E.Tchanga worked in the Department.

The most brilliant research achievements of the members of the Department include:

  • a new method of estimates of H.Weyl's sums and its applications in number theory;
  • an asymptotic formula for the number of representations of an odd integer by a sum of three prime numbers and, as corollary of this formula, the solution of the Goldbach problem;
  • the theory of trigonometric sums with prime numbers;
  • the solution of the 7th Hilbert problem on transcendency of logarithms of algebraic numbers;
  • rational approximations of linear forms of algebraic numbers and Diophantine equations;
  • the upper bound for the number of summands in the HilbertKamke problem;
  • elementary methods in additive problems with prime numbers;
  • the Waring problem and its generalizations to non-integer exponents;
  • the number theory methods in numerical analysis;
  • the large sieve and its applications.

Top
Research Directions

Nowadays the number theory research is concentrated on additive combinatorics: the theory of sum products, estimates on the cardinality of sets having no solutions of linear equations; analytic number theory: distribution of prime numbers, the theory of the Riemann zeta function and its generalizations, Gram&39;s law, the theory of Dirichlet characters, incomplete Kloosterman sums, power residues, different additive problems, the theory of automorphic $L$-series, convolution formulas.

Top
Main results

The members of the Department have made contribution to all main directions of analytic number theory as well as to some directions of applied mathematics, function theory, and algebraic geometry. In particular,

  • a local method of trigonometric sums was suggested which was used to construct a theory of multiple trigonometric sums similar to the classical Vinogradov's theory of Weyl's sums;
  • o problems about the exponent of convergence of singular integrals in the Tarry problem and its generalizations were solved;
  • the HilbertKamke problem and its generalizations to the multiple case were solved;
  • it was proved that strong forms of the Artin hypothesis on the number of variable forms or systems of forms, representing non-trivial zero in local fields are false;
  • a method of estimation of short sums of characters with modules equal to a power of a fixed prime number was discovered;
  • new elementary methods were developed in the theory of distribution of prime numbers and in the theory of equations over a finite field;
  • estimates of short sums of characters over shifted prime numbers in linear and non-linear case were obtained which are stronger than the results implied by the extended Riemann hypothesis;
  • the universality of the Riemann zeta-function and its generalizations was proved;
  • a new method of obtaining explicit formulae in additive problems of number theory was suggested;
  • a strong version of the Hilbert problem on differential independence of the Riemann zeta-function and its generalizations was proved;
  • the A. Selberg hypothesis on zeros of the Riemann zeta-function on short intervals of the critical line was proved;
  • a theorem about the `exclusiveness' of the critical line for zeros of the DavenportHeilbronn function and the Epstein zeta-function was proved;
  • on the basis of the Vinogradov method new properties of solutions of the Cauchy problem for Schroedinger type equations with periodic initial data were found and, in particular, a `quantum chaos' was discovered;
  • local and global properties of sums of trigonometric series with real algebraic polynomials in the index of imaginary exponent were studied;
  • algorithms of rapid multiplications of multi-digit numbers and of rapid calculation of elementary algebraic functions were found;
  • new quadrature formulae were constructed;
  • the three dimensional Luroth problem was solved;
  • a theory of rational surfaces over an algebraically non-closed field was developed and defining relations in the Cremona group of plane over an algebraically non-closed field were described;
  • the concept of birational rigidity, which is now one of the crucial concepts of higher dimensional birational geometry, was introduced and studied, a birational rigidity was proved for the main classes of higher dimensional Fano varieties and large classes of Fano fiber spaces.

Recent publications

| by years | scientific publications | by types |



   2018
1. I. D. Shkredov, “Prilozheniya teorii summ proizvedenii k mnozhestvam, izbegayuschim neskolko lineinykh uravnenii”, Matem. sb., 209 (2018) (to appear)  mathnet [I. D. Shkredov, “An application of the sum-product phenomenon to sets having no solutions to several linear equations”, Mat. Sb. (to appear)]

   2017
2. S. V. Konyagin, M. A. Korolev, “On irreducible solutions of an equation with reciprocals”, Mat. Sb., 2017 (to appear)  mathnet
3. Kevin Ford, Moubariz Z. Garaev, Sergei V. Konyagin, “On the smallest simultaneous power nonresidue modulo a prime”, Forum Math., 29:2 (2017), 347–355  mathnet  crossref  mathscinet  isi  scopus
4. Kevin Ford, Ben Green, Sergei Konyagin, James Maynard, Terence Tao, “Long gaps between primes”, J. Am. Math. Soc., 2017 (Published online) , arXiv: 1412.5029  mathnet  crossref
5. Analiticheskaya teoriya chisel, Sbornik statei. K 80-letiyu so dnya rozhdeniya Anatoliya Alekseevicha Karatsuby, Tr. MIAN, 299, ed. M. A. Korolëv, A. G. Sergeev, MAIK, M., 2017  mathnet
6. M. A. Korolev, (To be announced), On the occasion of the 80th anniversary of the birth of Professor Anatolii Alekseevich Karatsuba, Tr. Mat. Inst. Steklova, 299, MAIK Nauka/Interperiodica, Moscow, 2017 (to appear)  mathnet
7. M. A. Korolev, “Generalized Kloosterman sum with primes”, Proc. Steklov Inst. Math., 296 (2017), 154–171  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
8. K. Gong, C. Jia, M.A. Korolev, “Shifted character sums with multiplicative coefficients, II”, J. Number Theory, 178 (2017), 31–39 , arXiv: 1611.06577v1  mathnet  crossref  mathscinet  isi  scopus
9. M. A. Korolev, Analytic number theory, On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba, Tr. Mat. Inst. Steklova, 299, MAIK Nauka/Interperiodica, Moscow, 2017 (to appear)  mathnet
10. M. A. Korolev, “On Rieman–Siegel formula for the derivatives of Hardy's function”, Algebra i Analiz, 29:4 (2017), 53–81  mathnet  elib
11. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “On the Additive Energy of the Heilbronn Subgroup”, Math. Notes, 101:1 (2017), 58–70  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
12. Orit E. Raz, Micha Sharir, Ilya D. Shkredov, “On the number of unit-area triangles spanned by convex grids in the plane”, Comput. Geom., 62:1 (2017), 25–33  mathnet  crossref  mathscinet  isi  elib  scopus
13. A. S. Volostnov, I. D. Shkredov, “Sums of Multiplicative Characters with Additive Convolutions”, Proc. Steklov Inst. Math., 296 (2017), 256–269  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
14. I. D. Shkredov, “Neskolko zamechanii o mnozhestvakh s malym chastnym”, Matem. sb., 208:12 (2017) (to appear)  mathnet [I. D. Shkredov, “Some remarks on sets with small quotient set”, Mat. Sb. (to appear)]
15. I. S. Rezvyakova, “Additive Problem with the Coefficients of Hecke $L$-Functions”, Proc. Steklov Inst. Math., 296 (2017), 234–242  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
16. Olga Balkanova, Dmitry Frolenkov, “New error term for the fourth moment of automorphic $L$-functions”, J. Number Theory, 173 (2017), 293–303  mathnet  crossref  mathscinet  zmath  isi  scopus
17. V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formulae for the second moments of $L$-series of holomorphic cusp forms on the critical line”, Izv. Math., 81:2 (2017), 239–268  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
18. O. G. Balkanova, D. Frolenkov, “A note on the binary additive divisor problem”, (To be announced), On the occasion of the 80th anniversary of the birth of Professor Anatolii Alekseevich Karatsuba, Tr. Mat. Inst. Steklova, 299, MAIK Nauka/Interperiodica, Moscow, 2017 (to appear)  mathnet
19. V. A. Bykovskii, D. A. Frolenkov, “The average length of finite continued fractions with fixed denominator”, Sb. Math., 208:5 (2017), 644–683  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
20. Olga Balkanova, Dmitry Frolenkov, “Non-vanishing of automorphic $L$-functions of prime power level”, 2017, 1–25, arXiv: 1605.02434  mathnet  crossref  scopus

   2016
21. Sergei V. Konyagin, Florian Luca, Bernard Mans, Luke Mathieson, Min Sha, Igor E. Shparlinski, “Functional graphs of polynomials over finite fields”, J. Comb. Theory, Ser. B, 116 (2016), 87–122 , arXiv: 1307.2718  mathnet  crossref  mathscinet (cited: 1)  zmath  isi (cited: 2)  elib  scopus (cited: 2)
22. Kevin Ford, Ben Green, Sergei Konyagin, Terence Tao, “Large gaps between consecutive prime numbers”, Ann. of Math. (2), 183:3 (2016), 935–974 , arXiv: 1408.4505  mathnet  crossref  mathscinet (cited: 6)  zmath  isi (cited: 4)  elib  scopus (cited: 4)
23. S. V. Konyagin, A. A. Kuleshov, “On some properties of finite sums of ridge functions defined on convex subsets of $\mathbb R^n$”, Proc. Steklov Inst. Math., 293 (2016), 186–193  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus
24. S. V. Konyagin, M. A. Korolev, “On a symmetric diophantine equation with reciprocals”, Proc. Steklov Inst. Math., 294 (2016), 67–77  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus
25. S. V. Konyagin, I. D. Shkredov, “New results on sums and products in $\mathbb R$”, Proc. Steklov Inst. Math., 294 (2016), 78–88 , arXiv: 1602.03473  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus
26. A. A. Karatsuba, “Kosmologiya i Dzeta. Doklad v Moskve”, Teoriya chisel i prilozheniya, 1, K 80-letiyu so dnya rozhdeniya professora Anatoliya Alekseevicha Karatsuby, Sovr. probl. matem., 23, MIAN, M., 2016, 17–23  mathnet  crossref  elib; A. A. Karatsuba, “Cosmology and zeta”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 11–17  crossref  isi  scopus
27. A. A. Karatsuba, “O nulyakh nekotorykh ryadov Dirikhle. Doklad v Obervolfakhe”, Teoriya chisel i prilozheniya, 1, K 80-letiyu so dnya rozhdeniya professora Anatoliya Alekseevicha Karatsuby, Sovr. probl. matem., 23, MIAN, M., 2016, 12–16  mathnet  crossref  elib; A. A. Karatsuba, “On zeros of certain Dirichlet series”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 6–10  crossref  isi  scopus
28. A. A. Karatsuba, “O lokalnom predstavlenii nulya formoi. Doklad v Chandigarkhe”, Teoriya chisel i prilozheniya, 1, K 80-letiyu so dnya rozhdeniya professora Anatoliya Alekseevicha Karatsuby, Sovr. probl. matem., 23, MIAN, M., 2016, 7–11  mathnet  crossref  elib; A. A. Karatsuba, “On local representation of zero by a form”, Proc. Steklov Inst. Math., 296, suppl. 2 (2017), 1–5  crossref  isi  scopus
29. M. A. Korolev, “On non-linear Kloosterman sum”, Chebyshevskii Sb., 17:1 (2016), 140–147  mathnet  elib
30. M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus
31. M. A. Korolev, On Kloosterman sums with multiplicative coefficients, 2016 , 13 pp., arXiv: 1610.09171
32. M. A. Korolev, “Short Kloosterman Sums to Powerful Modulus”, Doklady Mathematics, 94:2 (2016), 561–562  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
33. M. A. Korolev, “Gram's Law in the Theory of Riemann Zeta-Function. Part 2”, Proc. Steklov Inst. Math., 294, suppl. 1 (2016), 1–78  mathnet  crossref  crossref  isi  elib  elib  scopus
34. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
35. M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Chebyshevskii Sb., 17:4 (2016), 79–109  mathnet  crossref  elib
36. Maxim Aleksandrovich Korolev, “An extreme values of the function S(T) in short intervals”, Indian J. Pure Appl. Math., 47:4 (2016), 603–615 , arXiv: 1302.0352  mathnet  crossref  zmath  isi  scopus
37. Tomasz Schoen, Ilya D. Shkredov, “Additive dimension and a theorem of sanders”, J. Aust. Math. Soc., 100:1 (2016), 124–144  mathnet  crossref  mathscinet (cited: 1)  isi  elib  scopus
38. S. V. Konyagin, I. D. Shkredov, New results on sum–products in $\mathbb R$, 2016 , 18 pp., arXiv: 1602.03473
39. Ilya D. Shkredov, “On a question of A. Balog”, Pacific J. Math., 280:1 (2016), 227–240  mathnet  crossref  mathscinet (cited: 2)  zmath  isi (cited: 1)  elib  scopus (cited: 1)
40. Oliver Roche-Newton, Misha Rudnev, Ilya D. Shkredov, “New sum-product type estimates over finite fields”, Adv. Math., 293 (2016), 589–605  mathnet  crossref  mathscinet (cited: 6)  zmath  isi (cited: 3)  elib  scopus (cited: 3)
41. Alex Samorodnitsky, Ilya Shkredov, Sergey Yekhanin, “Kolmogorov width of discrete linear spaces: An approach to matrix rigidity”, Comput. Complexity, 25:2 (2016), 309–348  mathnet  crossref  mathscinet  zmath  isi  elib  scopus
42. I. V. Vyugin, E. V. Solodkova, I. D. Shkredov, “Intersections of Shifts of Multiplicative Subgroups”, Math. Notes, 100:2 (2016), 189–198  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus
43. I. D. Shkredov, “Erratum to: On some problems of Euclidean Ramsey theory”, Anal. Math., 42:3 (2016), 295  mathnet  crossref  isi  scopus
44. I. D. Shkredov, Some remarks on sets with small quotient set, 2016 , 14 pp., arXiv: 1603.04948v2
45. Shkredov, I. D., “Difference sets are not multiplicatively closed”, Discrete Anal., 2016, 17 , 21 pp.  mathnet  crossref
46. Esen Aksoy Yazici, Brendan Murphy, Misha Rudnev, Ilya Shkredov, “Growth estimates in positive characteristic via collisions”, Int. Math. Res. Not. IMRN, 2016 (Published online) , 39 pp.  mathnet  crossref  adsnasa
47. I.D. Shkredov, “On tripling constant of multiplicative subgroups”, Integers, 16 (2016), 75 , 9 pp.  mathnet
48. Tomasz Schoen, Ilya D. Shkredov, “A remark on $A+B$ and $A-A$ for compact sets in $\mathbb R^n$”, Integers, 16 (2016), 60 , 4 pp.  mathnet
49. I. S. Rezvyakova, “On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach”, Izv. Math., 80:3 (2016), 602–622  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus
50. Olga G. Balkanova, Dmitry A. Frolenkov, “A uniform asymptotic formula for the second moment of primitive $L$-functions on the critical line”, Proc. Steklov Inst. Math., 294 (2016), 13–46  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus

   2015
51. S. R. Blackburn, S. V. Konyagin, I. E. Shparlinski, “Counting additive decompositions of quadratic residues in finite fields”, Funct. Approx. Comment. Math., 52:2 (2015), 223–227  mathnet  crossref  mathscinet  elib  scopus (cited: 1)
52. S. V. Konyagin, I. D. Shkredov, “A quantitative version of the Beurling-Helson theorem”, Funct. Anal. Appl., 49:2 (2015), 110–121 , arXiv: 1401.4429  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
53. S. V. Konyagin, A. A. Kuleshov, “On the Continuity of Finite Sums of Ridge Functions”, Math. Notes, 98:2 (2015), 336–338  mathnet  crossref  crossref  mathscinet  isi (cited: 3)  elib  elib  scopus
54. S. V. Konyagin, I. E. Shparlinski, “Quadratic non-residues in short intervals”, Proc. Amer. Math. Soc., 143:10 (2015), 4261–4269  mathnet  crossref  mathscinet (cited: 1)  zmath  isi  elib  scopus
55. S. V. Konyagin, I. D. Shkredov, “On Sum Sets of Sets Having Small Product Set”, Proc. Steklov Inst. Math., 290 (2015), 288–299  mathnet  crossref  crossref  isi (cited: 6)  elib  elib  scopus (cited: 5)
56. J. Bourgain, S. V. Konyagin, I. E. Shparlinski, “Character sums and deterministic polynomial root finding in finite fields”, Math. Comp., 84:296 (2015), 2969–2977 , arXiv: 1308.4803  mathnet  crossref  mathscinet (cited: 3)  zmath  isi  scopus
57. K. Ford, D. R. Heath-Brown, S. V. Konyagin, “Large gaps between consecutive prime numbers containing perfect powers”, Analytic Number Theory, In Honor of Helmut Maier's 60th Birthday, eds. C. Pomerance, M. Th. Rassias, Springer, New York, 2015, 83–92 , arXiv: 1411.6543  mathnet  crossref  scopus (cited: 2)
58. A. A. Karatsuba, “Vienna talk: on the number of zeros of the Riemann zeta function in short intervals of the critical line”, Chebyshevskii Sb., 16:1 (2015), 19–31  mathnet  elib
59. A. A. Karatsuba, “Moscow talk: the theorem on approximation of trigonometric sum by a short one (ATS)”, Chebyshevskii Sb., 16:1 (2015), 6–18  mathnet  elib
60. M. A. Korolev, “Large values of the Riemann zeta-function on short intervals of the critical line”, Dokl. Math., 91:1 (2015), 102–104  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 1)  elib  elib  scopus (cited: 1)
61. E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, V. N. Chubarikov, “On the conference to the memory of Anatoly Alexeevitch Karatsuba on number theory and applications”, Chebyshevskii Sb., 16:1 (2015), 89–152  mathnet  mathscinet  elib
62. M. A. Korolev, “On Incomplete Gaussian Sums”, Proc. Steklov Inst. Math., 290 (2015), 52–62  mathnet  crossref  crossref  isi  elib  elib  scopus
63. M. A. Korolev, “On the Horizontal Distribution of Zeros of the Functions $\operatorname{Re} \zeta(s)$ and $\operatorname{Im}\zeta(s)$”, Math. Notes, 98:6 (2015), 986–989  mathnet  crossref  crossref  mathscinet  isi  elib  scopus
64. M. A. Korolëv, Zakon Grama v teorii dzeta-funktsii Rimana. Ch. 1, Sovr. probl. matem., 20, MIAN, M., 2015 , 162 pp.  mathnet  mathnet  crossref  crossref  elib; M. A. Korolev, “Gram's Law in the Theory of Riemann Zeta-Function. Part 1”, Proc. Steklov Inst. Math., 292, suppl. 2 (2016), S1–S146  crossref  isi  elib  scopus
65. M. A. Korolev, “On the large values of the Riemann zeta-function on the critical line - II”, Mosc. J. Comb. Number Theory, 5:3 (2015), 60–86 http://mjcnt.phystech.edu/ru/article.php?id=99, arXiv: 1412.6340  adsnasa
66. M. A. Korolev, “On the primitive of Hardy's function”, The 29th Journees Arithmetiques. Conference handbook (University of Debrecen, Hungary, July 6–10, 2015), University of Debrecen, 2015, 57–58 http://www.ja2015.math.unideb.hu/sites/default/files/Abstracts.pdf
67. M. A. Korolev, “On the large values of the Riemann zeta-function on the critical line II”, Moscow J. Combin. Number Theory, 5:3 (2015), 60–86  mathnet  mathscinet  zmath  adsnasa
68. I. D. Shkredov, “Structure theorems in additive combinatorics”, Russian Math. Surveys, 70:1 (2015), 113–163  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
69. Brendan Murphy, Oliver Roche-Newton, Ilya Shkredov, “Variations on the sum-product problem”, SIAM J. Discrete Math., 29:1 (2015), 514–540  mathnet (cited: 1)  crossref  mathscinet (cited: 5)  zmath  isi (cited: 2)  elib (cited: 1)  scopus (cited: 3)
70. I. D. Shkredov, “On Sums of Szemerédi–Trotter Sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309  mathnet  crossref  crossref  isi (cited: 4)  elib  elib  scopus (cited: 1)
71. I. D. Shkredov, “On some problems of Euclidean Ramsey theory”, Anal. Math., 41:4 (2015), 299–310  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  scopus
72. G. I. Arkhipov, V. N. Chubarikov, “Anatoly Alekseevich Karatsuba”, Chebyshevskii Sb., 16:1 (2015), 32–51  mathnet  mathscinet  elib
73. I. S. Rezvyakova, “Selbergs method in the problem about the zeros of linear combinations of $L$-functions on the critical line”, Dokl. Math., 92:1 (2015), 448–451  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
74. I. S. Rezvyakova, “On the zeros of the Epstein zeta-function on the critical line”, Russian Math. Surveys, 70:4 (2015), 785–787  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib  scopus (cited: 1)
75. V. A. Bykovskii, D. A. Frolenkov, “Some integral representations of hypergeometric function”, FEMJ, 15:1 (2015), 38–40  mathnet  elib
76. D. A. Frolenkov, “On the uniform bounds on hypergeometric function”, Dal'nevost. Mat. Zh., 15:2 (2015), 289–298  mathnet  elib
77. V. A. Bykovskii, D. A. Frolenkov, “On the second moment of L-series of holomorphic cusp forms on the critical line”, Dokl. Math., 92:1 (2015), 417–420  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus
78. V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formula for the convolution of a generalized divisor function”, Dokl. Math., 92:3 (2015), 670–673  mathnet  crossref  crossref  isi (cited: 1)  elib  scopus (cited: 1)

   2014
79. S. V. Konyagin, “Double Exponential Lower Bound for the Number of Representations of Unity by Egyptian Fractions”, Math. Notes, 95:2 (2014), 280–284  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  elib  scopus (cited: 1)
80. S. V. Konyagin, “Deviation of Elements of a Banach Space from a System of Subspaces”, Proc. Steklov Inst. Math., 284 (2014), 204–207  mathnet  crossref  crossref  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
81. S. V. Konyagin, Yu. V. Malykhin, K. S. Ryutin, “Letter to the Editor”, Math. Notes, 96:3 (2014), 462  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
82. M. Z. Garaev, S. V. Konyagin, “Multiplicative decomposition of arithmetic progressions in prime fields”, J. Number Theory, 145 (2014), 540–553 , arXiv: 1309.6980  mathnet  crossref  mathscinet (cited: 1)  zmath  isi (cited: 7)  isi (cited: 7)  elib  scopus
83. J. Bourgain, M. G. Garaev, S. V. Konyagin, I. E. Shparlinski, “Multiplicative congruences with variables from short intervals”, J. Anal. Math., 124:1 (2014), 117–143 , arXiv: 1210.6429  mathnet  crossref  mathscinet (cited: 7)  zmath  isi (cited: 5)  elib (cited: 1)  scopus (cited: 3)
84. S. V. Konyagin, I. D. Shkredov, “O norme Vinera podmnozhestv $\mathbb Z_p$ promezhutochnogo razmera”, Fundament. i prikl. matem., 19:5 (2014), 75–87 , arXiv: 1403.8129  mathnet  mathscinet  zmath  elib; S. V. Konyagin, I. D. Shkredov, “On the Wiener norm of subsets of $\mathbb Z_p$ of medium size”, J. Math. Sci., 218:5 (2016), 599–608  crossref  mathscinet  zmath  elib  scopus
85. S. V. Konyagin, “$h$-fold sums from a set with few products”, Moscow J. Combin. Number Theory, 4:3 (2014), 14–20  mathnet
86. M. A. Korolev, “On small values of the Riemann zeta-function at Gram points”, Sb. Math., 205:1 (2014), 63–82  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib  elib  scopus
87. M. A. Korolev, “Moments of trigonometric polynomials and their applications in the theory of the Riemann zeta-function”, Dokl. Math., 89:3 (2014), 305–307  mathnet  crossref  crossref  mathscinet  zmath  isi  elib  elib  scopus
88. M. A. Korolev, “On large values of the Riemann zeta-function on short segments of the critical line”, Acta Arith., 166:4 (2014), 349–390 , arXiv: 1404.6649  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 2)  scopus (cited: 2)
89. T. Schoen, I. D. Shkredov, “Roth's theorem in many variables”, Israel J. Math., 199:1 (2014), 287–308 , arXiv: 1106.1601v1  mathnet  crossref  mathscinet (cited: 8)  zmath  isi (cited: 3)  scopus
90. I. D. Shkredov, “Sumsets in quadratic residues”, Acta Arith., 164:3 (2014), 221–243 , arXiv: 1305.4093v1  mathnet  crossref  mathscinet (cited: 5)  zmath  isi (cited: 7)  elib (cited: 3)  scopus (cited: 7)
91. I. D. Shkredov, “On exponential sums over multiplicative subgroups of medium size”, Finite Fields Appl., 30 (2014), 72–87  mathnet  crossref  mathscinet (cited: 9)  zmath  isi (cited: 11)  elib (cited: 8)  scopus (cited: 10)
92. I. Shkredov, “Energies and structure of additive sets”, Electron. J. Combin., 21:3 (2014), P3.44 , 53 pp.  mathnet  mathscinet (cited: 4)  zmath  isi  scopus (cited: 5)
93. I. S. Rezvyakova, An additive problem with the Fourier coefficients of holomorphic non-cusp forms, Conference Paper, 2014 , Presentation on the conference: Zeta Functions 5 (Moscow)  crossref
94. I. D. Kan, D. A. Frolenkov, “A strengthening of a theorem of Bourgain and Kontorovich”, Izv. Math., 78:2 (2014), 293–353  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 2)
95. D. A. Frolenkov, I. D. Kan, “A strengthening of a theorem of Bourgain–Kontorovich II”, Moscow J. Combin. Number Theory, 4:1 (2014), 78–117  mathnet  mathscinet  zmath

   2013
96. Ortogonalnye ryady, teoriya priblizhenii i smezhnye voprosy, Sbornik statei. K 60-letiyu so dnya rozhdeniya akademika Borisa Sergeevicha Kashina, Tr. MIAN, 280, ed. S. V. Konyagin, A. G. Sergeev, MAIK, M., 2013 , 303 pp.  mathnet
97. Proc. Steklov Inst. Math., 280 (2013), 61–90  mathnet  crossref  crossref  mathscinet  isi (cited: 7)  scopus (cited: 17)
98. O. V. Besov, S. V. Bochkarev, E. A. Volkov, V. A. Il'in, B. S. Kashin, V. V. Kozlov, S. V. Konyagin, N. N. Kudryavtsev, Yu. S. Osipov, S. I. Pokhozhaev, V. A. Sadovnichii, A. G. Sergeev, S. A. Telyakovskii, “His mathematical century (to the memory of Sergei Mikhailovich Nikol'skii)”, Russian Math. Surveys, 68:3 (2013), 591–594  mathnet  crossref  crossref  mathscinet  zmath  zmath  adsnasa  isi  elib
99. S. V. Konyagin, Yu. V. Malykhin, C. S. Rjutin, “On Exact Recovery of Sparse Vectors from Linear Measurements”, Math. Notes, 94:1 (2013), 107–114  mathnet  crossref  crossref  zmath  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
100. K. Gyarmati, S. Konyagin, A. Sárkősy, “On the reducibility of large sets of integers modulo $p$”, J. Number Theory, 133:7 (2013), 2374–2397  mathnet  crossref  mathscinet (cited: 4)  isi (cited: 3)  elib (cited: 3)  scopus (cited: 3)
101. S. Konyagin, M. Rudnev, “On new sum-product estimates”, SIAM J. Discrete Math., 27:2 (2013), 973–990  mathnet  crossref  mathscinet (cited: 15)  zmath  isi (cited: 9)  elib (cited: 8)  scopus (cited: 9)
102. K. Ford, S. Konyagin, Y. Lamzouri, “The prime number race and zeros of Dirichlet $L$-functions off the critical line: part 3”, Quarterly Journal of Mathematics, 64:4 (2013), 1091–1098  mathnet  crossref  mathscinet  isi (cited: 1)  scopus (cited: 1)
103. S. V. Konyagin, “Numbers that become composite after changing one or two digits”, Pioneer J. Algebra Number Theory Appl., 6:1 (2013), 1–7  mathnet
104. A. A. Karatsuba, “Comments to My Works,Written by Myself”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S1–S23  mathnet  crossref  crossref  isi  elib  scopus (cited: 1)
105. M. A. Korolev, “On new results related to Gram's law”, Izv. Math., 77:5 (2013), 917–940  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
106. F. Götze, D. Kaliada, M. Korolev, On the number of integral quadratic polynomials with bounded heights and discriminants, 2013 , 14 pp., arXiv: 1308.2091 (in Russian)  adsnasa
107. J. Kalpokas, M. A. Korolev, J. Steuding, “Negative values of the Riemann zeta function on the critical line”, Mathematika, 59:2 (2013), 443–462 , arXiv: 1109.2224v3  mathnet  crossref  mathscinet (cited: 5)  zmath  adsnasa  isi (cited: 4)  elib (cited: 5)  scopus (cited: 4)
108. M. A. Korolev, “On the moments of some trigonometric sums”, 28th Journees Arithmetiques, Programme and Abstract book (Grenoble, France, July 1–5, 2013), Institut Fourier - University Joseph Fourier, 2013, 58–59
109. M. A. Korolev, “On $L_p$-norms of certain trigonometric polynomials”, Palanga Conference in Combinatorics and Number Theory, Program and abstract book (Palanga, Lithuania, September 01–07, 2013), 2013, 24–26 http://mjcnt.phystech.edu/conference/palanga/abstract_book.pdf (Supported by Yandex, Vilnius University and Moscow Journal of Combinatorics and Number Theory)
110. M. A. Korolëv, Zakon Grama v teorii dzeta-funktsii Rimana, Avtoreferat diss. … dokt. fiz.-matem. nauk, MIAN, M., 2013 http://www.mi.ras.ru/dis/ref13/korolev_ref.pdf
111. T. Schoen, I. D. Shkredov, “Higher moments of convolutions”, J. Number Theory, 133 (2013), 1693–1737  mathnet  crossref  mathscinet (cited: 17)  zmath  isi (cited: 15)  elib (cited: 15)  scopus (cited: 15)
112. I. D. Shkredov, On exponential sums over multiplicative subgroups of medium size, 2013 , 14 pp., arXiv: 1311.5726
113. I. D. Shkredov, New bounds for Heilbronn's exponential sum, 2013 , 14 pp., arXiv: 1302.3839
114. I. D. Shkredov, “Some new results on higher energies”, Trans. Moscow Math. Soc., 2013 (2013), 31–63  mathnet  crossref  mathscinet  zmath  elib  scopus (cited: 5)
115. I. D. Shkredov, “On Heilbronn's exponential sum”, Q. J. Math., 64:4 (2013), 1221–1230  mathnet  crossref  mathscinet (cited: 7)  zmath  isi (cited: 9)  elib (cited: 7)  scopus (cited: 9)
116. I. D. Shkredov, “Some new inequalities in additive combinatorics”, Moscow J. Combin. Number Theory, 3:3 (2013), 189–239 , arXiv: 1208.2344v3  mathnet  elib
117. I. S. Rezvyakova, “Zeros of the Epstein zeta function on the critical line.”, Palanga Conference in Combinatorics and Number Theory (Palanga, 1–7 September 2013), Vilnius University, 2013, 47 http://mjcnt.phystech.edu/conference/palanga/abstract_book.pdf
118. Irina Rezvyakova, “Zeros of linear combinations of degree two L-functions on the critical line: Selberg's method”, Abstract book (28th Journées Arithmétiques, July 1–5, 2013, University Joseph Fourier Grenoble I, Grenoble, France), University Joseph Fourier Grenoble I, 2013, 74 http://at.yorku.ca/cgi-bin/abstract/cbhj-28
119. D. A. Frolenkov, K. Soundararajan, “A generalization of the Pólya–Vinogradov inequality”, Ramanujan J., 31:3 (2013), 271–279  mathnet  crossref  mathscinet (cited: 2)  zmath  isi (cited: 2)  scopus (cited: 2)

   2012
120. M. Z. Garaev, S. V. Konyagin, Yu. V. Malykhin, “Asymptotics for the sum of powers of distances between power residues modulo a prime”, Proc. Steklov Inst. Math., 276 (2012), 77–89  mathnet  crossref  mathscinet  isi (cited: 1)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)
121. T. Cochrane, S. Konyagin, “Proof of the Goresky Klapper conjecture on decimations of $L$-functions”, SIAM J. Disc. Math., 26:4 (2012), 1812–1831  mathnet  crossref  mathscinet  zmath  isi  scopus
122. T. Khovanova, S. Konyagin, “Sequences of integers with missing quotients and dense points without neighbors”, Discrete Mathematics, 312:10 (2012), 1776–1787  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib  scopus
123. J. Bourgain, S. V. Konyagin, I. E. Shparlinski, “Distribution of elements of cosets of small subgroups and applications”, Int. Math. Res. Notices, 2012:9 (2012), 1968–2009  mathnet  crossref  mathscinet (cited: 7)  zmath  isi (cited: 10)  elib (cited: 9)  scopus (cited: 10)
124. S. V. Konyagin, I. E. Shparlinski, “On the consecutive powers of a primitive root: gaps and exponential sums”, Mathematika, 58:1 (2012), 11–20  mathnet  crossref  mathscinet (cited: 8)  zmath  isi (cited: 8)  elib (cited: 8)  scopus (cited: 8)
125. S. V. Konyagin, Yu. V. Malykhin, “Basis sets in Banach spaces”, Nonlinear analysis: stability, approximation, and inequalities, in honor of Themistocles M. Rassias on the occasion of his 60-th birthday, Springer Optim. Appl., 68, Springer-Verlag, Berlin–Heidelberg–New York, 2012, 381–386  mathnet  crossref  mathscinet (cited: 1)  zmath  scopus
126. P. Acquaah, S. Konyagin, “On prime factors of odd perfect numbers”, International Journal of Number Theory, 8:6 (2012), 1537–1540  mathnet  crossref  mathscinet (cited: 2)  zmath  isi (cited: 1)  scopus (cited: 3)
127. J. Bourgain, M. Z. Garaev, S. V. Konyagin, I. E. Shparlinski, “On the hidden shifted power problem”, SIAM Journal of Computing, 41:6 (2012), 1524–1557 , arXiv: 1110.0812  mathnet  crossref  mathscinet (cited: 17)  zmath  isi (cited: 17)  scopus (cited: 17)
128. K. Ford, S. Konyagin, F. Luca, “On groups with perfect order subsets”, Moscow J. Combin. Number Theory, 2:4 (2012), 3–18  mathnet  mathscinet  zmath  elib
129. M. A. Korolev, “On Gram's law in the theory of the Riemann zeta function”, Izv. Math., 76:2 (2012), 275–309  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 4)
130. M. A. Korolev, “On Karatsuba's problem related to Gram's law”, Proc. Steklov Inst. Math., 276 (2012), 156–166  mathnet  crossref  mathscinet  isi (cited: 1)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)
131. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolëv, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Nauchnye dostizheniya Anatoliya Alekseevicha Karatsuby”, Matematika i informatika, 1, K 75-letiyu so dnya rozhdeniya Anatoliya Alekseevicha Karatsuby, Sovr. probl. matem., 16, MIAN, M., 2012, 7–30  mathnet  crossref  zmath  elib; S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S1–S22  crossref  zmath  isi  scopus
132. M. A. Korolev, “On the small values of the Riemann zeta-function on the critical line”, Elementare und Analytische Zahlentheorie [Elementary and Analytic Number Theory] (Germany, Schloß Schney, August 13–18, 2012), eds. T. Christ, N. Oswald, R. Steuding, J. Steuding, Universität Würzburg, Würzburg, 2012, 21–22
133. M. A. Korolev, “On Karatsubas problem concerning the divisor function”, Monatsh. Math., 168:3-4 (2012), 403–441 , arXiv: 1011.1391  mathnet  crossref  mathscinet  adsnasa  isi  elib  scopus
134. M. A. Korolev, “Gram's law and the argument of the Riemann zeta function”, Publ. Inst. Math. (Beograd) (N.S.), 92(106) (2012), 53–78 , arXiv: 1106.0516v2  mathnet  crossref  mathscinet (cited: 2)  zmath  adsnasa  isi (cited: 1)  scopus (cited: 1)
135. M. A. Korolev, “On some new results related to Gram's law”, Dokl. Math., 86:2 (2012), 661–662  mathnet  crossref  mathscinet  mathscinet  zmath  isi  elib  elib  scopus
136. M. A. Korolev, “On Selberg formulae related to Gram's law”, Sb. Math., 203:12 (2012), 1808–1816  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
137. I. D. Shkredov, T. Schoen, “Additive properties of multiplicative subgroups of $F_p$”, Quart. J. Math., 63:3 (2012), 713–722  mathnet  crossref  mathscinet (cited: 17)  zmath  isi (cited: 13)  elib (cited: 11)  scopus (cited: 14)
138. I. V. Vyugin, I. D. Shkredov, “On additive shifts of multiplicative subgroups”, Sb. Math., 203:6 (2012), 844–863  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib (cited: 6)  elib (cited: 6)  scopus (cited: 5)
139. I. D. Shkredov, “On the Gowers Norms of Certain Functions”, Math. Notes, 92:4 (2012), 554–569  mathnet  crossref  crossref  zmath  isi  elib  elib  scopus
140. F. S. Avdeev, G. I. Arkhipov, S. B. Gashkov, N. M. Dobrovol'skii, B. S. Kashin, I. I. Mel'nikov, M. P. Mineev, Yu. V. Nesterenko, S. M. Nikol'skii, A. N. Parshin, V. P. Platonov, Yu. V. Prokhorov, V. A. Sadovnichii, A. T. Fomenko, V. G. Chirskii, “Vladimir Nikolaevich Chubarikov (on his 60th birthday)”, Russian Math. Surveys, 67:1 (2012), 189–193  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
141. G. I. Arkhipov, S. B. Gashkov, M. P. Mineev, S. M. Nikol'skii, V. A. Sadovnichii, Diskr. Mat., 24:2 (2012), 4–20  mathnet  crossref  mathscinet  elib
142. I. Rezvyakova, On the critical line zeros of $L$-functions attached to automorphic cusp forms, 2012 , 20 pp., arXiv: 1212.2948
143. D. A. Frolenkov, “The mean value of Frobenius numbers with three arguments”, Izv. Math., 76:4 (2012), 760–819  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 3)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 2)
144. D. A. Frolenkov, “Asymptotic behaviour of the first moment of the number of steps in the by-excess and by-deficiency Euclidean algorithms”, Sb. Math., 203:2 (2012), 288–305  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)

   2011
145. O. V. Besov, S. V. Bochkarev, B. I. Golubov, A. A. Gonchar, M. I. D'yachenko, V. V. Kozlov, S. V. Konyagin, Yu. V. Malykhin, S. M. Nikol'skii, M. K. Potapov, V. A. Sadovnichii, S. A. Telyakovskii, “Boris Sergeevich Kashin (on his 60th birthday)”, Russian Math. Surveys, 66:4 (2011), 825–828  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
146. J. Bourgain, S. Dilworth, K. Ford, S. Konyagin, D. Kutzarova, “Explicit constructions of RIP matrices and related problems”, Duke Math. J., 159:1 (2011), 145–185  crossref  mathscinet (cited: 27)  zmath  isi (cited: 69)  elib (cited: 75)  scopus (cited: 95)
147. S. V. Konyagin, I. E. Shparlinski, “On convex hull of points on modular hyperbolas”, Moscow J. Combin. and Number Theory, 1:1 (2011), 43–51  mathscinet (cited: 4)  zmath
148. J. Bourgain, S. J. Dilworth, K. Ford, S. V. Konyagin, D. Kutzarova, “Explicit constructions of RIP matrices”, Proc. 43rsACM Symposium of the Theory of Computing, STOC, 2011, 637–644  mathscinet (cited: 2)
149. S. V. Konyagin, “O sistemakh vektorov s ravnymi rasstoyaniyami”, Trudy matematicheskogo tsentra imeni N. I. Lobachevskogo (Kazan, iyun – iyul 2011 goda), Kazanskoe matematicheskoe obschestvo, 2011, 204–209
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