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Korolev Maxim Aleksandrovich
(full list of publications)
| by years | scientific publications | by types |


Articles

1. M. A. Korolev, Mat. Sb. (to appear)  mathnet

  
2. M. A. Korolev, “On Kloosterman sums with multiplicative coefficients”, Izv. RAN. Ser. Mat. (to appear)  mathnet
3. M. A. Korolev, “Elementary estimate of Kloosterman sum over primes”, Mat. Zametki (to appear)  mathnet

   2017
4. S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Sb. Math., 208:12 (2017), 1818–1834  mathnet  crossref  crossref  mathscinet  adsnasa  isi (cited: 2)  elib  scopus
5. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib  scopus
6. M. A. Korolev, “Generalized Kloosterman sum with primes”, Proc. Steklov Inst. Math., 296 (2017), 154–171  mathnet  crossref  crossref  mathscinet  isi (cited: 1)  elib  scopus
7. 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 (cited: 1)
8. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  isi (cited: 1)  elib  elib  scopus
9. M. A. Korolev, “On Rieman–Siegel formula for the derivatives of Hardy's function”, Algebra i Analiz, 29:4 (2017), 53–81  mathnet  mathscinet  elib

   2016
10. M. A. Korolev, “On non-linear Kloosterman sum”, Chebyshevskii Sb., 17:1 (2016), 140–147  mathnet  mathscinet  elib
11. 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: 4)  elib  elib  scopus (cited: 1)
12. M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 4)  elib  elib  scopus
13. M. A. Korolev, “Short Kloosterman Sums to Powerful Modulus”, Doklady Mathematics, 94:2 (2016), 561–562  mathnet  crossref  crossref  zmath  isi (cited: 1)  elib  elib  scopus
14. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi (cited: 2)  elib  scopus
15. M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Chebyshevskii Sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
16. 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

   2015
17. 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)
18. M. A. Korolev, “On Incomplete Gaussian Sums”, Proc. Steklov Inst. Math., 290 (2015), 52–62  mathnet  crossref  crossref  isi (cited: 3)  elib  elib  scopus
19. 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

   2016
20. 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  mathnet  mathnet  crossref  crossref  crossref  isi (cited: 1)  elib  elib  scopus

   2015
21. 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 , arXiv: 1412.6340  mathnet  mathscinet  zmath  adsnasa

   2014
22. 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
23. 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 (cited: 1)  elib  elib  scopus
24. 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: 4)  elib (cited: 2)  scopus (cited: 4)

   2013
25. 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
26. 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: 5)  elib (cited: 5)  scopus (cited: 4)

   2012
27. 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: 6)  elib (cited: 5)  elib (cited: 5)  scopus (cited: 4)
28. 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: 2)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)
29. M. A. Korolev, “On Karatsuba’s problem concerning the divisor function”, Monatsh. Math., 168:3-4 (2012), 403–441 , arXiv: 1011.1391  mathnet  crossref  mathscinet  adsnasa  isi (cited: 1)  elib  scopus (cited: 1)
30. 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)
31. 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
32. 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)

   2010
33. M. A. Korolev, “Gram's law and Selberg's conjecture on the distribution of zeros of the Riemann zeta function”, Izv. Math., 74:4 (2010), 743–780  mathnet  crossref  crossref  mathscinet  zmath  zmath  adsnasa  isi (cited: 12)  elib (cited: 8)  elib (cited: 8)  scopus (cited: 6)
34. M. A. Korolev, “On the average number of power residues modulo a composite number”, Izv. Math., 74:6 (2010), 1225–1254  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
35. M. A. Korolev, “Short Kloosterman Sums with Weights”, Math. Notes, 88:3 (2010), 374–385  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  elib (cited: 3)  scopus (cited: 3)

   2008
36. M. A. Korolev, “Selberg's conjecture concerning the distribution of imaginary parts of zeros of the Riemann zeta function”, Dokl. Math., 78:1 (2008), 531–534  mathnet  crossref  mathscinet  zmath  isi (cited: 1)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)
37. M. A. Korolev, “On the integral of Hardy's function $Z(t)$”, Izv. Math., 72:3 (2008), 429–478  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 5)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
38. M. A. Korolev, “On large distances between consecutive zeros of the Riemann zeta-function”, Izv. Math., 72:2 (2008), 291–304  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 3)

   2007
39. M. A. Korolev, “On large distances between neighboring zeros of the Riemann zeta function”, Dokl. Math., 76:3 (2007), 940–943  mathnet  crossref  mathscinet  zmath  isi  elib  elib  scopus
40. M. A. Korolev, “On the primitive of the Hardy function $Z(t)$”, Dokl. Math., 75:2 (2007), 295–298  mathnet  crossref  mathscinet  zmath  isi (cited: 2)  elib (cited: 1)  elib (cited: 1)  scopus (cited: 1)
41. A. A. Karatsuba, M. A. Korolëv, “Priblizhenie trigonometricheskoi summy bolee korotkoi”, Dokl. RAN, 412:2 (2007), 159–161  mathnet (cited: 1)  mathscinet (cited: 3)  elib (cited: 3)
42. A. A. Karatsuba, M. A. Korolev, “A theorem on the approximation of a trigonometric sum by a shorter one”, Izv. Math., 71:2 (2007), 341–370  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 6)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)

   2006
43. M. A. Korolev, “On multiple zeros of the Riemann zeta function”, Izv. Math., 70:3 (2006), 427–446  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 3)  elib (cited: 2)  elib (cited: 2)  scopus (cited: 2)
44. A. A. Karatsuba, M. A. Korolev, “Behaviour of the argument of the Riemann zeta function on the critical line”, Russian Math. Surveys, 61:3 (2006), 389–482  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 18)  elib (cited: 10)  elib (cited: 10)  scopus (cited: 10)

   2005
45. M. A. Korolev, “Sign changes of the function $S(t)$ on short intervals”, Izv. Math., 69:4 (2005), 719–731  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 4)  elib (cited: 3)  elib (cited: 3)  scopus (cited: 3)
46. M. A. Korolev, “On large values of the function $S(t)$ on short intervals”, Izv. Math., 69:1 (2005), 113–122  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 8)  elib (cited: 4)  elib (cited: 4)  scopus (cited: 6)
47. A. A. Karatsuba, M. A. Korolev, “The argument of the Riemann zeta function”, Russian Math. Surveys, 60:3 (2005), 433–488  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 27)  elib (cited: 31)  elib (cited: 31)  scopus (cited: 21)

   2003
48. M. A. Korolev, “On the behavior of the function $S(t)$ at short intervals”, Dokl. Math., 67:3 (2003), 396–397  mathnet  mathscinet  zmath  isi (cited: 3)  elib (cited: 3)  scopus (cited: 3)
49. M. A. Korolev, “The argument of the Riemann zeta-function on the critical line”, Izv. Math., 67:2 (2003), 225–264  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 9)  elib (cited: 7)  scopus (cited: 6)

   2002
50. M. A. Korolev, “On the number of sign changes of the function $S(t)$ on a short interval”, Dokl. Math., 65:1 (2002), 58–59  mathnet  mathscinet  zmath  isi (cited: 5)  scopus
51. M. A. Korolev, “The Argument of the Riemann Zeta Function on the Critical Line”, Proc. Steklov Inst. Math., 239 (2002), 202–224  mathnet  mathscinet  zmath

   2001
52. M. A. Korolëv, “O raspredelenii obratnykh velichin po zadannomu modulyu”, Sovremennye issledovaniya v matematike i mekhanike, Trudy XXIII Konferentsii molodykh uchenykh mekhaniko-matematicheskogo fakulteta MGU (Moskva, MGU, 9–14 aprelya 2001 g.), v. II, Izd-vo Tsentra prikladnykh issledovanii pri mekhaniko-matematicheskom fakultete MGU, Moskva, 2001, 184–186

   2000
53. M. A. Korolev, “Incomplete Kloosterman sums and their applications”, Izv. Math., 64:6 (2000), 1129–1152  mathnet  crossref  crossref  mathscinet  zmath  isi (cited: 8)  scopus (cited: 5)

   1998
54. M. A. Korolev, “On a new multiplicative function”, Russian Math. Surveys, 53:4 (1998), 868–869  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi (cited: 1)  scopus

Books


   2016
55. 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  mathscinet  isi  elib  elib  scopus

Thesis


   2013
56. 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

Proceedings


   2017
57. M. A. Korolev, “On the estimates of Kloosterman sums”, Vilnius Conference in Combinatoris and Number Theory, Program and Abstract book (Vilnius, Lithuania, July 16 - July 22, 2017), Vilnius University, 2017, p. 14. http://mjcnt.phystech.edu/conference/vilnius/Vilnius2017.pdf
58. M. A. Korolev, “Obratnye vychety v posledovatelnosti Pyatetskogo-Shapiro”, Konferentsiya po teorii chisel i prilozheniyam v chest 80-letiya A.A.Karatsuby, Sbornik annotatsii (Moskva, 22 - 27 maya 2017 g.), eds. M. A. Korolev, OOO “Poligraff”, 2017, s. 34. http://www.mathnet.ru/ConfLogos/936/abstracts.pdf

   2015
59. 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

   2013
60. 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
61. 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)

   2012
62. 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

   2011
63. 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
64. 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

ArXiv


   2016
65. M. A. Korolev, On Kloosterman sums with multiplicative coefficients, 2016 , 13 pp., arXiv: 1610.09171

   2013
66. 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

Научно-популярные и образовательные материалы


   2011
67. M. A. Korolëv, “Sodokladchiki”, My – matematiki s Leninskikh gor, Vypusk № 5 «V. I. Arnold», Moskva, 2011, 312

   2007
68. M. A. Korolev, “Esche raz o posledovatelnostyakh Rachinskogo”, Nauka i zhizn, 2007, no. 10, 89–91 (http://www.nkj.ru/archive/articles/11844/)

Information matherials


   2015
69. 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

Personalia


   2013
70. 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  mathnet  crossref  crossref  zmath  isi  elib  scopus

Miscellaneous


   2017
71. 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 , 303 pp.  mathnet

Letters, errata


   2011
72. M. A. Korolev, “Letter to the editors”, Izv. Math., 75:4 (2011), 869  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib  scopus
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