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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, Corresponding Member 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., Leading 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. A. 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 |


   2017
1. K. Ford, M. Z. Garaev, S. V. Konyagin, “On the smallest simultaneous power nonresidue modulo a prime”, Forum Mathematicum, 2017 (to appear) , arXiv: 1511.08428

   2016
2. 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  zmath  isi  elib  scopus
3. S. V. Konyagin, I. D. Shkredov, New results on sum–products in $\mathbb R$, 2016 , 18 pp., arXiv: 1602.03473
4. S. V. Konyagin, I. D. Shkredov, Modern problems of mathematics, mechanics, and mathematical physics. Part II, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016 (to appear)  mathnet
5. S. V. Konyagin, M. A. Korolev, Modern problems of mathematics, mechanics, and mathematical physics. Part II, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016 (to appear)  mathnet
6. Kevin Ford, Ben Green, Sergei Konyagin, Terence Tao, “Large gaps between consecutive prime numbers”, Annals of Mathematics, 183:3 (2016), 935–974 , arXiv: 1408.4505  mathnet  crossref  zmath  isi (cited: 1 \citnumescopus 1)  scopus
7. 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  elib  scopus
8. M. A. Korolev, “On non-linear Kloosterman sum”, Chebyshevskii Sb., 17:1 (2016), 140–147  mathnet  elib
9. M. A. Korolev, Gram's Law in the Theory of Riemann Zeta-Function. Part 2, Sovrem. Probl. Mat., 21, Steklov Math. Institute of RAS, Moscow, 2016 , 94 pp.  mathnet  mathnet  crossref  crossref
10. M. A. Korolev, Mat. Zametki, 2016 (to appear)  mathnet
11. M. A. Korolev, “On Karatsuba's method of estimating Kloosterman sums”, Mat. Sb., 207:8 (2016), 117–134  mathnet  crossref
12. Tomasz Schoen, Ilya D. Shkredov, “Additive dimension and a theorem of sanders”, J. Aust. Math. Soc., 100:1 (2016), 124–144  mathnet  crossref  mathscinet  isi  scopus
13. Ilya D. Shkredov, “On a question of A. Balog”, Pacific J. Math., 280:1 (2016), 227–240  mathnet  crossref  mathscinet  zmath  isi  scopus
14. 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  zmath  isi  scopus
15. 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  scopus
16. 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  elib
17. I. S. Rezvyakova, “On the zeros of linear combinations of L-functions of degree two on the critical line. Selberg's approach”, Izv. RAN. Ser. Mat., 80:3 (2016), 151–172  mathnet  crossref  mathscinet  elib
18. O. G. Balkanova, D. A. Frolenkov, Modern problems of mathematics, mechanics, and mathematical physics. Part II, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016 (to appear)  mathnet

   2015
19. 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
20. 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
21. 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: 1)  elib  elib  scopus
22. 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
23. 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  elib  elib  scopus
24. 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  zmath  isi
25. 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 \citnumescopus 1  mathnet  crossref  scopus
26. 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
27. 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
28. 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  elib  elib  scopus
29. 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
30. M. A. Korolev, “On Incomplete Gaussian Sums”, Proc. Steklov Inst. Math., 290 (2015), 52–62  mathnet  crossref  crossref  isi  elib  elib  scopus
31. 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  isi  elib  scopus
32. M. A. Korolëv, “Gram's Law in the Theory of Riemann Zeta-Function. Part 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  scopus
33. 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
34. 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
35. 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
36. 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  zmath  isi (cited: 1 \citnumescopus 1)  elib  scopus
37. I. D. Shkredov, “On Sums of Szemerédi–Trotter Sets”, Proc. Steklov Inst. Math., 289 (2015), 300–309  mathnet  crossref  crossref  isi (cited: 2)  elib  elib  scopus
38. I. D. Shkredov, “On some problems of Euclidean Ramsey theory”, Anal. Math., 41:4 (2015), 299–310  mathnet  crossref  mathscinet  zmath  isi  scopus
39. G. I. Arkhipov, V. N. Chubarikov, “Anatoly Alekseevich Karatsuba”, Chebyshevskii Sb., 16:1 (2015), 32–51  mathnet  mathscinet  elib
40. 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
41. 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  elib  scopus
42. V. A. Bykovskii, D. A. Frolenkov, “Some integral representations of hypergeometric function”, FEMJ, 15:1 (2015), 38–40  mathnet  elib
43. D. A. Frolenkov, “On the uniform bounds on hypergeometric function”, Dal'nevost. Mat. Zh., 15:2 (2015), 289–298  mathnet  elib
44. 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  elib  elib  scopus
45. 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  elib  scopus

   2014
46. 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  elib  elib  scopus
47. S. V. Konyagin, “Deviation of Elements of a Banach Space from a System of Subspaces”, Proc. Steklov Inst. Math., 284 (2014), 204–207 \citnumescopus 1  mathnet  crossref  crossref  isi  elib  elib  scopus
48. 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
49. M. Z. Garaev, S. V. Konyagin, “Multiplicative decomposition of arithmetic progressions in prime fields”, J. Number Theory, 145 (2014), 540–553 , arXiv: 1309.6980  crossref  mathscinet  zmath  isi  elib  scopus
50. 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  crossref  mathscinet (cited: 1)  isi (cited: 2 \citnumescopus 1)  elib  scopus
51. K. Ford, B. Green, S. Konyagin, J. Maynard, T. Tao, Long gaps between primes, 2014 , 39 pp., arXiv: 1412.5029
52. S. Konyagin, “$h$-fold sums from a set with few products”, Mosc. J. Comb. Number Theory, 4:3 (2014), 14–20 (288–294)
53. 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  elib
54. 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
55. 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  crossref  crossref  mathscinet  isi  elib  elib  scopus
56. 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  crossref  zmath  isi (cited: 1)  elib (cited: 1 \citnumescopus 1)  scopus
57. T. Schoen, I. D. Shkredov, “Roth's theorem in many variables”, Israel J. Math., 199:1 (2014), 287–308 , arXiv: 1106.1601v1  crossref  mathscinet (cited: 2)  zmath  isi (cited: 3)  scopus
58. I. D. Shkredov, “Sumsets in quadratic residues”, Acta Arith., 164:3 (2014), 221–243 , arXiv: 1305.4093v1  crossref  mathscinet (cited: 4)  zmath  isi (cited: 2)  elib (cited: 3 \citnumescopus 3)  scopus
59. I. D. Shkredov, “On exponential sums over multiplicative subgroups of medium size”, Finite Fields Appl., 30 (2014), 72–87  crossref  mathscinet (cited: 2)  zmath  isi (cited: 7)  elib (cited: 4 \citnumescopus 7)  scopus
60. I. Shkredov, “Energies and structure of additive sets”, Electron. J. Combin., 21:3 (2014), P3.44 , 53 pp.  mathscinet (cited: 1)  zmath  isi  scopus
61. 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
62. 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: 2)  elib (cited: 1 \citnumescopus 1)  elib (cited: 1 \citnumescopus 1)  scopus
63. D. A. Frolenkov, I. D. Kan, “A strengthening of a theorem of Bourgain-Kontorovich II”, Mosc. J. Comb. Number Theory, 4:1 (2014), 78–117

   2013
64. 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
65. Proc. Steklov Inst. Math., 280 (2013), 61–90  mathnet  crossref  crossref  mathscinet  isi (cited: 4 \citnumescopus 16)  scopus
66. 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
67. 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 \citnumescopus 1)  elib (cited: 1 \citnumescopus 1)  scopus
68. K. Gyarmati, S. Konyagin, A. Sárkősy, “On the reducibility of large sets of integers modulo $p$”, J. Number Theory, 133:7 (2013), 2374–2397  crossref  mathscinet (cited: 4)  isi (cited: 3)  elib (cited: 3 \citnumescopus 3)  scopus
69. S. Konyagin, M. Rudnev, “On new sum-product estimates”, SIAM J. Discrete Math., 27:2 (2013), 973–990  crossref  mathscinet (cited: 6)  zmath  isi (cited: 8)  elib (cited: 5 \citnumescopus 8)  scopus
70. 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  crossref  isi (cited: 1 \citnumescopus 1)  scopus
71. S. V. Konyagin, “Numbers that become composite after changing one or two digits”, Pioneer Journal of Algebra and Number Theory and Applications, 6:1 (2013), 1–7
72. A. A. Karatsuba, “Comments to My Works,Written by Myself”, Proc. Steklov Inst. Math., 282, suppl. 1 (2013), S1–S23 \citnumescopus 1  mathnet  crossref  crossref  isi  elib  scopus
73. 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
74. M. A. Korolev, Upper and lower bounds for the function $S(t)$ on the short intervals, 2013 , 11 pp., arXiv: 1302.0352  adsnasa
75. 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
76. 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  crossref  mathscinet (cited: 3)  zmath  adsnasa  isi (cited: 4)  elib (cited: 3 \citnumescopus 4)  scopus
77. 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
78. 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)
79. 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
80. T. Schoen, I. D. Shkredov, “Higher moments of convolutions”, J. Number Theory, 133 (2013), 1693–1737  crossref  mathscinet (cited: 11)  zmath  isi (cited: 13)  elib (cited: 12 \citnumescopus 13)  scopus
81. I. D. Shkredov, “Some new inequalities in additive combinatorics”, Mosc. J. Comb. Number Theory, 3:3-4 (2013), 189–239 [425–475] , arXiv: 1208.2344v3  elib
82. I. D. Shkredov, On exponential sums over multiplicative subgroups of medium size, 2013 , 14 pp., arXiv: 1311.5726
83. I. D. Shkredov, New bounds for Heilbronn's exponential sum, 2013 , 14 pp., arXiv: 1302.3839
84. I. D. Shkredov, “Some new results on higher energies”, Trans. Moscow Math. Soc., 2013 (2013), 31–63  mathnet  crossref  mathscinet  zmath  elib
85. I. D. Shkredov, “On Heilbronn's exponential sum”, Q. J. Math., 64:4 (2013), 1221–1230  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 5 \citnumescopus 7)  scopus
86. 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
87. 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
88. D. A. Frolenkov, K. Soundararajan, “A generalization of the Pólya–Vinogradov inequality”, Ramanujan J., 31:3 (2013), 271–279  crossref  mathscinet  zmath  isi (cited: 1 \citnumescopus 1)  scopus

   2012
89. 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 \citnumescopus 2)  elib (cited: 2 \citnumescopus 2)  scopus
90. T. Cochrane, S. Konyagin, “Proof of the Goresky Klapper conjecture on decimations of $L$-functions”, SIAM J. Disc. Math., 26:4 (2012), 1812–1831  crossref  mathscinet  zmath  isi  scopus
91. T. Khovanova, S. Konyagin, “Sequences of integers with missing quotients and dense points without neighbors”, Discrete Mathematics, 312:10 (2012), 1776–1787  crossref  mathscinet  zmath  isi  elib  scopus
92. 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  crossref  mathscinet (cited: 4)  zmath  isi (cited: 8)  elib (cited: 5 \citnumescopus 8)  scopus
93. S. V. Konyagin, I. E. Shparlinski, “On the consecutive powers of a primitive root: gaps and exponential sums”, Mathematika, 58:1 (2012), 11–20  crossref  mathscinet (cited: 3)  zmath  isi (cited: 7)  elib (cited: 3 \citnumescopus 8)  scopus
94. 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  zmath  scopus
95. P. Acquaah, S. Konyagin, “On prime factors of odd perfect numbers”, International Journal of Number Theory, 8:6 (2012), 1537–1540  crossref  mathscinet (cited: 1)  zmath  isi (cited: 1 \citnumescopus 3)  scopus
96. 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  crossref  mathscinet (cited: 12)  zmath  isi (cited: 14 \citnumescopus 12)  scopus
97. K. Ford, S. Konyagin, F. Luca, “On groups with perfect order subsets”, Mosc. J. Comb. Number Theory, 2:4 (2012), 3–18 [297–312]  mathscinet (cited: 2)  elib
98. 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 \citnumescopus 4)  elib (cited: 5 \citnumescopus 4)  scopus
99. 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 \citnumescopus 2)  elib (cited: 2 \citnumescopus 2)  scopus
100. S. A. Gritsenko, E. A. Karatsuba, M. A. Korolëv, I. S. Rezvyakova, D. I. Tolev, M. E. Changa, “Scientific Achievements of Anatolii Alekseevich Karatsuba”, 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
101. 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
102. M. A. Korolev, “On Karatsubas problem concerning the divisor function”, Monatsh. Math., 168:3-4 (2012), 403–441 , arXiv: 1011.1391  crossref  mathscinet  adsnasa  isi  elib  scopus
103. 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  crossref  mathscinet  zmath  adsnasa  isi (cited: 1 \citnumescopus 1)  scopus
104. M. A. Korolev, “On some new results related to Gram's law”, Dokl. Math., 86:2 (2012), 661–662  crossref  mathscinet  zmath  isi  elib  elib  scopus
105. 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 \citnumescopus 1)  elib (cited: 1 \citnumescopus 1)  scopus
106. I. D. Shkredov, T. Schoen, “Additive properties of multiplicative subgroups of $F_p$”, Quart. J. Math., 63:3 (2012), 713–722  crossref  mathscinet (cited: 12)  isi (cited: 10)  elib (cited: 10 \citnumescopus 11)  scopus
107. 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: 2)  elib (cited: 6 \citnumescopus 4)  elib (cited: 6 \citnumescopus 4)  scopus
108. 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
109. 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
110. 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
111. I. Rezvyakova, On the critical line zeros of $L$-functions attached to automorphic cusp forms, 2012 , 20 pp., arXiv: 1212.2948
112. 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: 2)  elib (cited: 3 \citnumescopus 2)  elib (cited: 3 \citnumescopus 2)  scopus
113. 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 \citnumescopus 1)  elib (cited: 1 \citnumescopus 1)  scopus

   2011
114. 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
115. 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: 19)  zmath  isi (cited: 49)  elib (cited: 55 \citnumescopus 74)  scopus
116. 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: 1)  zmath
117. 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: 1)
118. 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
119. S. V. Konyagin, Yu. V. Malykhin and V. N. Temlyakov, “On basis sets in Banach spaces”, East J. Approx., 17 (2011), 215–220  mathscinet  zmath
120. S. V. Konyagin, A. Yu. Popov, “On the reconstruction of functions from the values of the $n$th differences with step $1/n$”, Tr. IMM UrO RAN, 17, no. 3, 2011, 178–185  mathnet; S. V. Konyagin, A. Yu. Popov, “On the reconstruction of functions from the values of the $n$th differences with step $1/n$”, Proc. Steklov Inst. Math. (Suppl.), 277, Suppl. 1 (2012), 113–120  crossref  isi  scopus
121. V. V. Arestov, V. I. Berdyshev, N. I. Chernykh, T. V. Demina, N. N. Kholschevnikova, S. V. Konyagin, Yu. N. Subbotin, S. A. Telyakovskii, I. G. Tsar'kov, V. A. Yudin, “Exposition of the lectures by S. B. Stechkin on approximation theory”, Eurasian Math. J., 2:4 (2011), 5–155  mathnet (cited: 1)  mathscinet  zmath
122. A. A. Karatsuba, “A property of the set of primes as a multiplicative basis of the natural numbers”, Dokl. Math., 84:1 (2011), 467–470  crossref  mathscinet  zmath  isi (cited: 2)  elib  elib  scopus
123. A. A. Karatsuba, “A property of the set of prime numbers”, Russian Math. Surveys, 66:2 (2011), 209–220  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 2)  elib  elib  scopus
124. M. A. Korolev, “Letter to the editors”, Izv. Math., 75:4 (2011), 869  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
125. M. Korolev, “On Gram's law in the theory of Riemann zeta function”, Mezhdunarodnaya konferentsiya «Diofantovy priblizheniya. Sovremennoe sostoyanie i prilozheniya» (3–8 iyulya 2011 g., Minsk, Belarus), Tezisy dokladov, Institut matematiki NAN Belarusi, Minsk, 2011, 37–38
126. M. A. Korolev, “Gram's law in the theory of Riemann's zeta function”, 27th Journees Arithmetiques (2011/06/27–07/01, Vilnius, Lithuania), Programme and Abstract book, Vilnius University, Vilnius, Lithuania, 2011, 34
127. M. A. Korolëv, “Sodokladchiki”, My – matematiki s Leninskikh gor, Vypusk № 5 «V. I. Arnold», Moskva, 2011, 312
128. I. D. Shkredov, S. Yekhanin, “Sets with large additive energy and symmetric sets”, J. Combin. Theory Ser. A, 118:3 (2011), 1086–1093  crossref  mathscinet (cited: 3)  zmath  isi (cited: 4)  elib (cited: 3 \citnumescopus 3)  scopus
129. I. D. Shkredov, T. Schoen, “On sumsets of convex sets”, Comb. Probab. Comput., 20 (2011), 793–798  crossref  mathscinet (cited: 9)  zmath  isi (cited: 11)  elib (cited: 11 \citnumescopus 15)  scopus
130. I. D. Shkredov, “Some applications of W. Rudins inequality to problems of combinatorial Number theory”, Uniform Distribution Theory, 6:2 (2011), 95–116 http://www.boku.ac.at/math/udt/vol06/no2/08Shkredov11-2.pdf  mathscinet (cited: 3)
131. G. I. Arkhipov, V. N. Chubarikov, Chebyshevskii Sb., 12:4 (2011), 39–42  mathnet  mathscinet  elib
132. G. I. Arkhipov, S. B. Gashkov, M. P. Mineev, N. M. Dobrovol'skii, Chebyshevskii Sb., 12:4 (2011), 4–14  mathnet  mathscinet  elib
133. G. I. Arkhipov, V. N. Chubarikov, Chebyshevskii Sb., 12:1 (2011), 4–9  mathnet  mathscinet  elib
134. I. S. Rezvyakova, “On the zeros of Hecke $L$-functions and their linear combinations on the critical line”, 27th Journées Arithmétiques (June 27 – July 1, 2011, Vilnius, Lithuania), Vilnius University, Vilnius, Lithuania, 2011
135. D. A. Frolenkov, “A numerically explicit version of the Pólya-Vinogradov inequality”, Mosc. J. Comb. Number Theory, 1:3 (2011), 25–41  mathscinet (cited: 1)  zmath  elib
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