Persons: Korolev, Maxim Aleksandrovich

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Korolev, Maxim Aleksandrovich

Statistics
in MathSciNet:	83 (79)
in zbMATH:	56 (54)
in Web of Science:	69 (66)
in Scopus:	73 (71)

Corresponding member of RAS

Doctor of physico-mathematical sciences (2013)

Speciality:

01.01.06 (Mathematical logic, algebra, and number theory)

Birth date:

19.03.1978

E-mail:

Keywords:

Kloostermann sums, argument of the Riemann zeta-function, Grams rule.

UDC:

511, 517, 511.33, 511.21, 511.331

MSC:

11L03, 11N37, 11M06, 11M26, 11L05, 11N37, 11M06

Subject:

Estimation of short Kloosterman sums, Riemanns zeta-function theory.

Biography

Graduated from Faculty of Mathematics and Mechanics of M. V. Lomonosov Moscow State University (MSU) in 2000 (department of mathematical analysis).

Main publications:

Korolev M. A., “Nepolnye summy Kloostermana i ikh prilozheniya”, Izv. RAN. Ser. matem., 64:6 (2000), 41–64
M.A. Korolev, “O pervoobraznoi funktsii Khardi $Z(t)$”, Izv. RAN. Ser. matem., 72:3 (2008), 19-68
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

https://www.mathnet.ru/eng/person8879

List of publications on Google Scholar

https://zbmath.org/authors/ai:korolev.maxim-a

https://mathscinet.ams.org/mathscinet/MRAuthorID/643508

https://elibrary.ru/author_items.asp?authorid=198334

https://www.webofscience.com/wos/author/record/Q-4405-2016

https://www.scopus.com/authid/detail.url?authorId=7005718404

https://www.researchgate.net/profile/M_Korolev

List of publications:

scientific publications

by years

by types

by times cited

common list

		Citations (Crossref Cited-By Service + Math-Net.Ru)

1.	A. A. Karatsuba, M. A. Korolev, “The argument of the Riemann zeta function”, Russian Math. Surveys, 60:3 (2005), 433–488
2.	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
3.	M. A. Korolev, “Incomplete Kloosterman sums and their applications”, Izv. Math., 64:6 (2000), 1129–1152
4.	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
5.	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
6.	M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158
7.	M. A. Korolev, “Short Kloosterman Sums with Weights”, Math. Notes, 88:3 (2010), 374–385
8.	M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659
9.	Maxim Korolev, Igor Shparlinski, “Sums of algebraic trace functions twisted by arithmetic functions”, Pacific J. Math., 304:2 (2020), 505–522 , arXiv: 1804.01337	11 ^[x]
10.	Maxim Korolev, Antanas Laurinčikas, “A new application of the Gram points”, Aequationes Math., 93:5 (2019), 859–873	11 ^[x]
11.	M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827
12.	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
13.	M. A. Korolev, “On large values of the function $S(t)$ on short intervals”, Izv. Math., 69:1 (2005), 113–122
14.	M. A. Korolev, “On Gram's law in the theory of the Riemann zeta function”, Izv. Math., 76:2 (2012), 275–309
15.	M. A. Korolev, “The argument of the Riemann zeta-function on the critical line”, Izv. Math., 67:2 (2003), 225–264
16.	M. A. Korolev, “Generalized Kloosterman sum with primes”, Proc. Steklov Inst. Math., 296 (2017), 154–171
17.	S. V. Konyagin, M. A. Korolev, “On a symmetric diophantine equation with reciprocals”, Proc. Steklov Inst. Math., 294 (2016), 67–77
18.	M. A. Korolev, “On the integral of Hardy's function $Z(t)$”, Izv. Math., 72:3 (2008), 429–478
19.	M. A. Korolev, “Short Kloosterman Sums to Powerful Modulus”, Doklady Mathematics, 94:2 (2016), 561–562
20.	M. A. Korolev, “The Argument of the Riemann Zeta Function on the Critical Line”, Proc. Steklov Inst. Math., 239 (2002), 202–224
21.	M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661
22.	M. A. Korolev, “Methods of estimating of incomplete Kloosterman sums”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 230–245
23.	Maxim Korolev, Antanas Laurinčikas, “A new application of the Gram points. II”, Aequationes Math., 94 (2020), 1171–1187	6 ^[x]
24.	S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Sb. Math., 208:12 (2017), 1818–1834
25.	M. A. Korolev, “On non-linear Kloosterman sum”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 246–249
26.	M. A. Korolev, “On Incomplete Gaussian Sums”, Proc. Steklov Inst. Math., 290 (2015), 52–62
27.	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	6 ^[x]
28.	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	6 ^[x]
29.	M. A. Korolev, “On multiple zeros of the Riemann zeta function”, Izv. Math., 70:3 (2006), 427–446
30.	M. A. Korolev, “Sign changes of the function $S(t)$ on short intervals”, Izv. Math., 69:4 (2005), 719–731
31.	Maxim Korolev, Antanas Laurinčikas, “Joint approximation of analytic functions by shifts of the Riemann zeta-function twisted by the Gram function”, Carpathian J. Math., 39:1 (2023), 175–187	5 ^[x]
32.	M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142
33.	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
34.	Maxim Korolev, Antanas Laurinčikas, “On the approximation by Mellin transform of the Riemann zeta-function”, Axioms, 12:6 (2023), 520 , 19 pp.	4 ^[x]
35.	M. A. Korolev, “Short Kloosterman Sums with Primes”, Math. Notes, 106:1 (2019), 89–97
36.	M. A. Korolev, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Math. Notes, 103:5 (2018), 761–768
37.	M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170
38.	M. A. Korolev, “On small values of the Riemann zeta-function at Gram points”, Sb. Math., 205:1 (2014), 63–82
39.	M. A. Korolev, “On new results related to Gram's law”, Izv. Math., 77:5 (2013), 917–940
40.	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	4 ^[x]
41.	M. A. Korolev, “On Selberg formulae related to Gram's law”, Sb. Math., 203:12 (2012), 1808–1816
42.	M. A. Korolev, “On the behavior of the function $S(t)$ at short intervals”, Dokl. Math., 67:3 (2003), 396–397
43.	M. A. Korolev, M. E. Changa, “New Estimate for Kloosterman Sums with Primes”, Math. Notes, 108:1 (2020), 87–93
44.	M. A. Korolev, “On Karatsuba’s problem concerning the divisor function”, Monatsh. Math., 168:3-4 (2012), 403–441 , arXiv: 1011.1391	3 ^[x]
45.	M. A. Korolev, “On the average number of power residues modulo a composite number”, Izv. Math., 74:6 (2010), 1225–1254
46.	M. A. Korolev, “On large distances between consecutive zeros of the Riemann zeta-function”, Izv. Math., 72:2 (2008), 291–304
47.	M. A. Korolev, D. A. Popov, “On Jutila's integral in the circle problem”, Izv. Math., 86:3 (2022), 413–455
48.	K. Gong, C. Jia, M.A. Korolev, “Shifted character sums with multiplicative coefficients, II”, J. Number Theory, 178 (2017), 31–39 , arXiv: 1611.06577v1	2 ^[x]
49.	M. A. Korolev, “On Rieman–Siegel formula for the derivatives of Hardy's function”, St. Petersburg Math. J., 29:4 (2018), 581–601
50.	M. A. Korolev, “On Karatsuba's problem related to Gram's law”, Proc. Steklov Inst. Math., 276 (2012), 156–166
51.	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
52.	Maxim Korolev, Antanas Laurinčikas, “Joint functional independence of the Riemann zeta-function”, Indian J. Pure Appl. Math., 56 (2025), 1523–1528	1 ^[x]
53.	M. A. Korolev, “A distribution related to Farey series”, Chebyshevskii Sb., 24:4 (2023), 137–190
54.	M. A. Korolev, “Vinogradov's sieve and an estimate for an incomplete Kloosterman sum”, Sb. Math., 213:2 (2022), 216–234
55.	S. V. Konyagin, M. A. Korolev, “On Titchmarsh's Phenomenon in the Theory of the Riemann Zeta Function”, Proc. Steklov Inst. Math., 319 (2022), 168–187 (to appear)
56.	Maxim Korolev, Antanas Laurinčikas, “Gram points in the theory of zeta-functions of certain cusp forms”, J. Math. Anal. Appl., 504:1 (2021), 125396 , 18 pp.	1 ^[x]
57.	Maxim A. Korolev, “Kloosterman sums over primes of composite moduli”, Res. Number Theory, 6 (2020), 24 , 20 pp.	1 ^[x]
58.	M. A. Korolev, “Kloosterman sums with primes and the solvability of one congruence with inverse residues — II”, Chebyshevskii sb., 21:1 (73) (2020), 200–211	1 ^[x]
59.	M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43
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
61.	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
62.	M. A. Korolev, “On large distances between neighboring zeros of the Riemann zeta function”, Dokl. Math., 76:3 (2007), 940–943
63.	A. A. Karatsuba, M. A. Korolëv, “Priblizhenie trigonometricheskoi summy bolee korotkoi”, Dokl. RAN, 412:2 (2007), 159–161	1 ^[x]
64.	M. A. Korolev, “On the period of the continued fraction expansion for $\sqrt{d}$”, Izv. Math., 89:1 (2025), 26–49
65.	M. A. Korolev, “Ob odnom raspredelenii, svyazannom s ryadami Fareya - II”, Chebyshevskii sbornik, 26:3 (2025), 136-173 (to appear) , arXiv: https://arxiv.org/abs/2503.08176
66.	M. A. Korolev, “Residue designs modulo a given number on the circle”, Math. Notes, 116:5 (2024), 1020–1041
67.	M. A. Korolev, “Konstruktsii na okruzhnosti, obrazovannye vychetami”, Mezhdunarodnaya konferentsiya «Matematika v sozvezdii nauk». K yubileyu rektora MGU akademika Viktora Antonovicha Sadovnichego: Tezisy dokladov. (Moskva, 1-2 aprelya 2024 g.), Izdatelstvo Moskovskogo universiteta, 2024, 54–55 (Published online) https://disk.yandex.ru/i/YJ84z2l1UMrIjQ
68.	M. A. Korolev, An upper bound for the second moment of the length of the period of the continued fraction expansion for $\sqrt{d}$, 2024 , 23 pp., arXiv: 2403.08616
69.	M. A. Korolev, “Arifmeticheskie svoistva “obobschennykh drobei Fareya””, Konferentsiya po kompleksnomu analizu i ego prilozheniyam (g. Krasnoyarsk, 11-15 sentyabrya 2023 g.), eds. K. V. Reznikova, Sibirskii federalnyi universitet, g. Krasnoyarsk, 2023, 34
70.	M. A. Korolev, “Ob odnom tozhdestve Ramanudzhana i ego obobscheniyakh”, Algebra, teoriya chisel, diskretnaya geometriya i mnogomasshtabnoe modelirovanie: sovremennye problemy, prilozheniya i problemy istorii Materialy XXII Mezhdunarodnoi konferentsii, posvyaschennoi 120-letiyu so dnya rozhdeniya akademika A. N. Kolmogorova i 60-letiyu so dnya otkrytiya shkoly-internata # 18 pri Moskovskom universitete., Biblioteka Chebyshevskogo sbornika (Tula, 26–29 sentyabrya 2023 goda), 350 s. ISBN 5–87954–388–9., Tula: Tul. gos. ped. un-t im. L. N. Tolstogo, 2023, 8–11 http://poivs.tsput.ru/conf/international/XXII/files/Conference2023S.pdf?v=3
71.	M. A. Korolev, I. S. Rezvyakova, “O sovmestnykh priblizheniyakh logarifmov prostykh chisel”, Chebyshevskii sb., 23:5 (2022), 87–100
72.	M. A. Korolev, “O nekotorykh arifmeticheskikh svoistvakh drobei Fareya”, Vtoraya konferentsiya Matematicheskikh tsentrov Rossii (7–11 noyabrya 2022 g.): sbornik tezisov. (Moskva, 7–11 noyabrya 2022 g.), Izdatelstvo Moskovskogo universiteta, Moskva, 2022, 123–126 https://www.mathnet.ru/ConfLogos/2047/Sbornik_tezisov.pdf
73.	M. A. Korolev, “Kloosterman Sums with Primes and Solvability of a Congruence with Inverse Residues”, Proc. Steklov Inst. Math., 314 (2021), 96–126
74.	A. T. Daniyarkhodzhaev, M. A. Korolev, “On a Ramanujan Identity and Its Generalizations”, Math. Notes, 110:4 (2021), 511–521
75.	M. A. Korolev, I. S. Rezvyakova, “Incomplete Kloosterman sums to prime power modules”, Bull., Cl. Sci. Math. Nat., Sci. Math., 46 (2021), 73–92
76.	M. A. Korolev, A. V. Shubin, “The second moment of the first derivative of Hardy’s $Z$-function”, Trigonometric Sums and Their Applications, eds. A. Raigorodskii, M. T. Rassias, Springer Nature Switzerland AG, 2020, 169–182
77.	V. M. Buchstaber, M. A. Korolev, “On the scientific works of Dmitry Alexandrovich Popov”, Chebyshevskii Sb., 21:4 (2020), 396–421
78.	M. A. Korolev, A. V. Ustinov, “Distribution of rational points on the circle of unit radius”, Izv. Math., 83:5 (2019), 1008–1049
79.	M. A. Korolev, Kloosterman sums with primes to composite moduli, 2019 , 23 pp., arXiv: 1911.09981
80.	M. E. Changa, M. A. Korolev, Kloosterman sums with primes and the solvability of one congruence with inverse residues. I, 2019 , 38 pp., arXiv: 1911.12589
81.	M. A. Korolev, “O razreshimosti v prostykh chislakh nekotorykh sravnenii s obratnymi velichinami”, Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy, prilozheniya i problemy istorii: Materialy XVI Mezhdunarodnoi konferentsii, posvyaschennoi 80-letiyu so dnya rozhdeniya professora Mishelya Deza (Tula, 13-18 maya 2019 g.), Biblioteka Chebyshevskogo sbornika, eds. V. N. Chubarikov, N. M. Dobrovolskii, I. Yu. Rebrova,N. N. Dobrovolskii, Tul. gos. ped. un-t im. L.N. Tolstogo, 2019, 37–39
82.	M. A. Korolev, “Ob odnom obschem svoistve ryadov Fareya”, Algebra, teoriya chisel i matematicheskoe modelirovanie dinamicheskikh sistem: Tezisy Mezhdunarodnoi konferentsii «Algebra, teoriya chisel i matematicheskoe modelirovanie dinamicheskikh sistem», posvyaschennoi 70-letiyu A.Kh. Zhurtova (Nalchik, 29 iyunya - 3 iyulya 2019 g.), Nalchik: Izd-vo KBGU, 2019, 2019, 58–59 http://algebra.imm.uran.ru/conf-algebra/algebra/trudy2019.pdf
83.	Alexandar P. Ivić, Maxim A. Korolev, “On the distribution of values of the argument of the Riemann zeta-function”, J. Number Theory, 200 (2019), 96–131 , arXiv: 1808.10768
84.	M. A. Korolev, A. V. Ustinov, “The Distribution of the Rational Points on the Unit Circle”, Dokl. Math., 98:1 (2018), 321–324
85.	M. A. Korolev, I. E. Shparlinski, Sums of algebraic trace functions twisted by arithmetic functions, 2018 , 19 pp., arXiv: 1804.01337
86.	M. A. Korolev, “Raspredelenie ratsionalnykh tochek na edinichnoi okruzhnosti (po sovmestnoi rabote s A. V. Ustinovym)”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii "Aktualnye problemy prikladnoi matematiki (Kabardino-Balkarskaya respublika, pos.Terskol, 22–26 maya 2018 g.), IPMA KBNTs RAN, Nalchik, 2018, 130
87.	M. A. Korolev, “Ob odnom raspredelenii, svyazannom s drobyami Fareya”, "Algebra, teoriya chisel i diskretnaya geometriya: sovremennye problemy i prilozheniya. Materialy XV Mezhdunarodnoi konferentsii, posvyaschennoi stoletiyu so dnya rozhdeniya professora Nikolaya Mikhailovicha Korobova (Tula, 28–31 maya 2018 g.), Seriya “Biblioteka Chebyshevskogo sbornika”, TPGU im. L.N. Tolstogo, Tula, 2018, 34-36
88.	M. A. Korolev, “The estimate of weighted Kloosterman sums by additive shift”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 221–229
89.	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
90.	M. A. Korolëv, “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. Korolëv, OOO “Poligraff”, 2017, s. 34. http://www.mathnet.ru/ConfLogos/936/abstracts.pdf
91.	M. A. Korolev, On Kloosterman sums with multiplicative coefficients, 2016 , 13 pp., arXiv: 1610.09171
92.	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
93.	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
94.	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
95.	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
96.	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
97.	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)
98.	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
99.	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)
100.	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
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 some new results related to Gram's law”, Dokl. Math., 86:2 (2012), 661–662
103.	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
104.	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
105.	M. A. Korolev, “On the primitive of the Hardy function $Z(t)$”, Dokl. Math., 75:2 (2007), 295–298
106.	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
107.	M. A. Korolev, “On a new multiplicative function”, Russian Math. Surveys, 53:4 (1998), 868–869
108.	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
109.	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
110.	M. A. Korolev, Vvedenie v metod resheta, Letnyaya shkola “Sovremennaya matematika”, MTsNMO, Moskva, 2024 , 56 pp.
111.	N. N. Andreev, M. A. Vsemirnov, S. O. Gorchinskiy, D. N. Zaporozhets, S. V. Kislyakov, V. V. Kozlov, M. A. Korolev, D. O. Orlov, Yu. S. Osipov, D. V. Treschev, P. A. Yaskov, “Steklov Institute – 90!”, Russian Math. Surveys, 79:3 (2024), 557–562
112.	T.G.Bobkina, M. A. Korolev, “I. M. Vinogradov at Saint Petersburg Emperor University: to the problem stating”, Chebyshevskii Sb., 24:2 (2023), 284–293
113.	M. A. Korolev, “Udivlyayuschaya prostota. O dostizheniyakh Dzheimsa Meinarda”, Troitskii variant, 2022, no. 14 (358), 26 iyulya 2022 g., 7 http://trv-science.ru/uploads/358N.pdf
114.	M. Korolev, Kvant, 2021, no. 8, 2–9
115.	T. G. Bobkina, M. A. Korolev, “K 130-letiyu I.M. Vinogradova”, Kvant, 2021, no. 9, 13–15
116.	M. A. Korolev, “Obmanchivaya prostota prostykh chisel”, Kvant, 2020, no. 3, 10–17
117.	M. A. Korolev, “Letter to the editors”, Izv. Math., 75:4 (2011), 869
118.	M. A. Korolëv, “Sodokladchiki”, My – matematiki s Leninskikh gor, Vypusk № 5 «V. I. Arnold», Moskva, 2011, 312
119.	M. A. Korolev, “Esche raz o posledovatelnostyakh Rachinskogo”, Nauka i zhizn, 2007, no. 10, 89–91 (http://www.nkj.ru/archive/articles/11844/)
120.	Analiticheskaya i kombinatornaya teoriya chisel, Sbornik statei. K 130-letiyu so dnya rozhdeniya akademika Ivana Matveevicha Vinogradova, Trudy MIAN, 314, ed. D. V. Treschev, S. V. Konyagin, V. N. Chubarikov, M. A. Korolev, M. R. Gabdullin, MIAN, M., 2021 , 346 pp.
121.	Analiticheskaya teoriya chisel, Sbornik statei. K 80-letiyu so dnya rozhdeniya Anatoliya Alekseevicha Karatsuby, Trudy MIAN, 299, ed. M. A. Korolev, A. G. Sergeev, MAIK «Nauka/Interperiodika», M., 2017 , 303 pp.

Presentations in Math-Net.Ru

1.	О периоде разложения $\sqrt{D}$ в цепную дробь M. A. Korolev Annual Session of Steklov Mathematical Institute (Best results 2025) November 18, 2025 10:40
2.	On the properties of the Farey transform M. A. Korolev International conference «Selected topics of function theory» dedicated to the 80th anniversary of Eugenie M. Nikishin September 30, 2025 11:00
3.	Как изучают дроби Фарея M. A. Korolev Contemporary Problems in Number Theory March 27, 2025 12:30
4.	Арифметика и геометрия дробей Фарея. Семинар 4 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 27, 2024 15:30
5.	Арифметика и геометрия дробей Фарея. Семинар 3 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 25, 2024 11:15
6.	Арифметика и геометрия дробей Фарея. Семинар 2 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 23, 2024 11:15
7.	Арифметика и геометрия дробей Фарея. Семинар 1 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2024 July 22, 2024 17:15
8.	Отдел теории чисел S. V. Konyagin, M. A. Korolev Conference MIAN-90, dedicated to the 90th anniversary of Steklov Mathematical Institute May 13, 2024 10:00
9.	Дизайны на окружности Максим Королёв Mathematical seminar Faculty of Computer Science HSE March 1, 2024 18:10
10.	Дизайны на окружности M. A. Korolev Contemporary Problems in Number Theory February 29, 2024 12:45
11.	Around the Bombieri–Vinogradov theorem. Lecture 4 M. A. Korolev Mini-courses of the thematic program "Analysis and approximation theory" December 1, 2023 12:30
12.	Around the Bombieri–Vinogradov theorem. Lecture 3 M. A. Korolev Mini-courses of the thematic program "Analysis and approximation theory" December 1, 2023 11:00
13.	Об одном тождестве Рамануджана и его обобщениях M. A. Korolev Contemporary Problems in Number Theory November 30, 2023 12:45
14.	Обобщение одного тождества Рамануджана M. A. Korolev Memorial conference dedicated to the memory of A.N. Parshin November 28, 2023 16:20
15.	Around the Bombieri–Vinogradov theorem. Lecture 2 M. A. Korolev Mini-courses of the thematic program "Analysis and approximation theory" November 27, 2023 12:30
16.	Around the Bombieri–Vinogradov theorem. Lecture 1 M. A. Korolev Mini-courses of the thematic program "Analysis and approximation theory" November 27, 2023 11:00
17.	Арифметические свойства «обобщённых дробей Фарея» M. A. Korolev September 20, 2023 14:30
18.	Арифметические свойства «обобщённых дробей Фарея» M. A. Korolev Conference on Complex Analysis and its Applications September 12, 2023 10:00
19.	Дзета-функция Римана и простые числа. Семинар 4 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023 July 28, 2023 11:15
20.	Дзета-функция Римана и простые числа. Семинар 3 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023 July 27, 2023 09:30
21.	Дзета-функция Римана и простые числа. Семинар 2 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023 July 26, 2023 11:15
22.	Дзета-функция Римана и простые числа. Семинар 1 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023 July 24, 2023 15:30
23.	Воспоминания об Алексее Николаевиче Паршине V. L. Popov, F. A. Bogomolov, B. S. Kashin, A. G. Sergeev, M. A. Korolev, S. O. Gorchinskiy, I. A. Panin “Numbers and functions” – Memorial conference for 80th birthday of Alexey Nikolaevich Parshin December 1, 2022 16:30
24.	Решето И. М. Виноградова и оценка неполной суммы Клоостермана M. A. Korolev Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2022 November 23, 2022 13:00
25.	О локальной теореме Кронекера (по совместной работе с И.С.Резвяковой). M. A. Korolev Contemporary Problems in Number Theory November 17, 2022 12:45
26.	О некоторых арифметических свойствах дробей Фарея M. A. Korolev November 11, 2022 11:00
27.	Чудеса в решете, или как отсеивали простые числа Эратосфен, Брун, Сельберг. Семинар 4 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2022 July 29, 2022 11:15
28.	Чудеса в решете, или как отсеивали простые числа Эратосфен, Брун, Сельберг. Семинар 3 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2022 July 27, 2022 15:30
29.	Чудеса в решете, или как отсеивали простые числа Эратосфен, Брун, Сельберг. Семинар 2 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2022 July 25, 2022 11:15
30.	Чудеса в решете, или как отсеивали простые числа Эратосфен, Брун, Сельберг. Семинар 1 M. A. Korolev Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2022 July 23, 2022 15:30
31.	О больших значениях дзета-функции Римана на критической прямой M. A. Korolev Number theory and Geometry. Alexey Zykin Memorial Conference June 16, 2022 12:15
32.	Метод А. А. Карацубы оценок сумм Клоостермана и его развитие M. A. Korolev XXI International Conference «Algebra, Number Theory, Discrete Geometry and Multiscale Modeling: Modern Problems, Applications and Problems of History», Dedicated to the 85th Anniversaryof the Birth of A. A. Karatsuba May 17, 2022 15:55
33.	Lecture 12. Number Theory M. A. Korolev Number Theory December 1, 2021 14:45
34.	Lecture 11. Number Theory M. A. Korolev Number Theory November 24, 2021 14:45
35.	Lecture 10. Number Theory M. A. Korolev Number Theory November 17, 2021 14:45
36.	Lecture 9. Number Theory M. A. Korolev Number Theory November 10, 2021 14:45
37.	Lecture 8. Number Theory M. A. Korolev Number Theory November 3, 2021 14:45
38.	Lecture 7. Number Theory M. A. Korolev Number Theory October 27, 2021 14:45
39.	What we know and what we do not know about the zeros of Riemann zeta-function M. A. Korolev Beijing–Moscow Mathematics Colloquium October 22, 2021 11:00
40.	Lecture 6. Number Theory M. A. Korolev Number Theory October 20, 2021 14:45
41.	Lecture 5. Number Theory M. A. Korolev Number Theory October 13, 2021 14:45
42.	Lecture 4. Number Theory M. A. Korolev Number Theory October 6, 2021 14:45
43.	Lecture 3. Number Theory M. A. Korolev Number Theory September 29, 2021 14:45
44.	Lecture 2. Number Theory M. A. Korolev Number Theory September 22, 2021 14:45
45.	Titchmarsh phenomenon in the theory of Riemann zeta-function (joint work with S.V. Konyagin) M. A. Korolev Memorial Conference on Analytic Number Theory and Applications Dedicated to the 130th Anniversary of I. M. Vinogradov September 14, 2021 11:15
46.	Lecture 1. Number Theory M. A. Korolev Number Theory September 8, 2021 14:45
47.	Основы кругового метода в теории чисел. Семинар 3 М. А. Королёв Summer School "Contemporary Mathematics" Named After Vitaly Arnold, 2021 July 28, 2021 15:30
48.	Основы кругового метода в теории чисел. Семинар 2 М. А. Королёв Summer School "Contemporary Mathematics" Named After Vitaly Arnold, 2021 July 27, 2021 11:15
49.	Основы кругового метода в теории чисел. Семинар 1 М. А. Королёв Summer School "Contemporary Mathematics" Named After Vitaly Arnold, 2021 July 25, 2021 15:30
50.	Основы кругового метода в теории чисел. Лекция М. А. Королёв Summer School "Contemporary Mathematics" Named After Vitaly Arnold, 2021 July 23, 2021 11:15
51.	Об интеграле Ютилы в проблеме круга (по совместной работе с Д.А.Поповым) M. A. Korolev Contemporary Problems in Number Theory December 10, 2020 12:45
52.	Lecture 13. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" December 3, 2020 18:00
53.	Lecture 12. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" November 26, 2020 18:00
54.	Lecture 11. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" November 19, 2020 18:00
55.	Lecture 10. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" November 12, 2020 18:00
56.	Lecture 9. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" November 5, 2020 18:00
57.	Lecture 8. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" October 29, 2020 18:00
58.	Lecture 7. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" October 22, 2020 18:00
59.	Lecture 6. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" October 15, 2020 18:00
60.	Lecture 5. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" October 8, 2020 18:00
61.	Lecture 4. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" October 1, 2020 18:00
62.	Lecture 3. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" September 24, 2020 18:00
63.	Lecture 2. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" September 17, 2020 18:00
64.	Lecture 1. Sieve methods: selected topics M. A. Korolev Course by M. A. Korolev "Sieve methods: selected topics" September 10, 2020 18:00
65.	Лекция 15. Применение линейного решета M. A. Korolev Course by M. A. Korolev "Sieve methods" May 28, 2020
66.	Лекция 14. Линейное решето (окончание) M. A. Korolev Course by M. A. Korolev "Sieve methods" May 21, 2020
67.	Лекция 13. Линейное решето (продолжение) M. A. Korolev Course by M. A. Korolev "Sieve methods" May 14, 2020
68.	Лекция 12. Линейное решето (начало) M. A. Korolev Course by M. A. Korolev "Sieve methods" May 7, 2020
69.	Лекция 11. Приложение решета Сельберга к некоторым задачам с простыми числами M. A. Korolev Course by M. A. Korolev "Sieve methods" April 30, 2020
70.	Лекция 10. Решето Сельберга. Функция $G(z)$ (окончание) M. A. Korolev Course by M. A. Korolev "Sieve methods" April 23, 2020
71.	Лекция 9. Решето Сельберга. Функция $G(z)$ M. A. Korolev Course by M. A. Korolev "Sieve methods" April 16, 2020
72.	Лекция 8. Применение методов решета к задаче о больших делителях “сдвинутых” простых чисел M. A. Korolev Course by M. A. Korolev "Sieve methods" April 9, 2020
73.	Лекция 7. Решето Сельберга M. A. Korolev Course by M. A. Korolev "Sieve methods" April 2, 2020
74.	Лекция 6. Применение методов решета к задаче о больших расстояниях между соседними простыми числами. Теорема Эрдеша-Ранкина M. A. Korolev Course by M. A. Korolev "Sieve methods" March 26, 2020
75.	Лекция 5. Решето Бруна. Нижняя оценка M. A. Korolev Course by M. A. Korolev "Sieve methods" March 19, 2020 18:00
76.	Лекция 4. Решето Бруна. Приложения M. A. Korolev Course by M. A. Korolev "Sieve methods" March 12, 2020 18:00
77.	Лекция 3. Решето Бруна - Хооли. Верхняя оценка M. A. Korolev Course by M. A. Korolev "Sieve methods" March 5, 2020 18:00
78.	Лекция 2. Простейшее решето Бруна M. A. Korolev Course by M. A. Korolev "Sieve methods" February 20, 2020 18:00
79.	Лекция 1.Основные свойства простых чисел. Решето Эратосфена M. A. Korolev Course by M. A. Korolev "Sieve methods" February 13, 2020 18:00
80.	Короткие промежутки между простыми числами специального вида (по работе А.В.Шубина) M. A. Korolev Contemporary Problems in Number Theory December 26, 2019 12:45
81.	Суммы Клоостермана с простыми числами и их применение M. A. Korolev Traditional winter session MIAN–POMI devoted to the topic "Analysis" December 20, 2019 10:00
82.	What is known and what is unknown about zeros of Riemann zeta-function M. A. Korolev Automorphic forms and their applications November 26, 2019 18:00
83.	Distribution of rational points on the circle of unit radius M. A. Korolev Scientific session of the Steklov Mathematical Institute of RAS dedicated to the results of 2019 November 20, 2019 12:15
84.	О разрешимости в простых числах некоторых сравнений с обратными величинами M. A. Korolev Contemporary Problems in Number Theory May 16, 2019 12:45
85.	On a solvability of some congruences with reciprocals in prime numbers M. A. Korolev XVI International Conference «Algebra, Number Theory and Discrete Geometry: modern problems, applications and problems of history» dedicated to the 80th anniversary of the birth of Professor Michel Desa May 14, 2019 10:40
86.	Incomplete Kloosterman sums and solvability of some congruences with prime variables M. A. Korolev Мemorial conference dedicated to the memory of Ivan Matveevich Vinogradov March 28, 2019 15:30
87.	An analogue of “Gibbs phenomenon” in the theory of Riemann zeta-function M. A. Korolev Steklov Mathematical Institute Seminar December 20, 2018 16:00
88.	О новых эффектах, связанных с дзета-функцией Римана M. A. Korolev Knots and Representation Theory November 27, 2018 18:30
89.	On the zeros of Epstein zeta-function, Kloosterman sums and some other problems of number theory M. A. Korolev Conference «Contemporary Mathematics and its applications» dedicated to the results of research supported by the Russian Science Foundation grant 14-50-00005 November 19, 2018 14:00
90.	A distribution connected with Farey fractions M. A. Korolev XV International Conference «Algebra, Number Theory and Discrete Geometry: modern problems and applications», dedicated to the centenary of the birth of the Doctor of Physical and Mathematical Sciences, Professor of the Moscow State University Korobov Nikolai Mikhailovich May 30, 2018 09:00
91.	Дроби Фарея и рациональные точки на окружности M. A. Korolev Contemporary Problems in Number Theory December 7, 2017 12:45
92.	Inverse residues and Pyatetski-Shapiro sequences M. A. Korolev А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications May 24, 2017 11:30
93.	Суммы Клоостермана: метод Бургейна. Лекци 9 M. A. Korolev November 24, 2016
94.	Суммы Клоостермана: метод Бургейна. Лекция 8 M. A. Korolev November 17, 2016 18:00
95.	Суммы Клоостермана: метод Бургейна. Лекция 7 M. A. Korolev November 10, 2016 18:00
96.	Суммы Клоостермана: метод Бургейна. Лекция 6 M. A. Korolev November 3, 2016 18:00
97.	Суммы Клоостермана: метод Бургейна. Лекция 5 M. A. Korolev October 27, 2016 18:00
98.	Суммы Клоостермана: метод Бургейна. Лекция 4 M. A. Korolev October 20, 2016 18:00
99.	Суммы Клоостермана: метод Бургейна. Лекция 3 M. A. Korolev October 6, 2016 18:00
100.	Суммы Клоостермана: метод Бургейна. Лекция 2 M. A. Korolev September 29, 2016 18:00
101.	Об оценках обобщенных сумм Клоостермана M. A. Korolev International conference on number theory and analysis, dedicated to the 125th anniversary of I. M. Vinogradov September 28, 2016 14:00
102.	Суммы Клоостермана: метод Бургейна. Лекция 1 M. A. Korolev September 22, 2016 18:00
103.	Аналитическая теория чисел в работах П. Л. Чебышева M. A. Korolev Internet video conference "Day of Mathematics and Mechanics" September 12, 2016 11:55
104.	Karatsuba's method of estimating of short Kloosterman sums M. A. Korolev Conference to the Memory of Anatoly Alekseevitch Karatsuba on Number theory and Applications January 28, 2016 12:00
105.	О дробных моментах некоторых теоретико-числовых функций (Fractional moments of some number-theoretic functions) M. A. Korolev Contemporary Problems in Number Theory July 31, 2014 12:45
106.	О больших значениях дзета-функции Римана на коротких промежутках критической прямой M. A. Korolev Shafarevich Seminar June 3, 2014 15:00
107.	Моменты тригонометрических полиномов M. A. Korolev Shafarevich Seminar April 30, 2013 15:00
108.	О моментах специальных тригонометрических полиномов M. A. Korolev Contemporary Problems in Number Theory March 28, 2013 12:45
109.	On the small values of the Riemann zeta-function on the critical line M. A. Korolev International Chinese-Russian conference on Number Theory October 8, 2012 16:00
110.	Некоторые задачи дискретной теории дзета-функции Римана M. A. Korolev Contemporary Problems in Number Theory April 19, 2012 12:45
111.	О законе Грама в теории дзета-функции Римана M. A. Korolev Seminar by Algebra Department March 13, 2012 15:00
112.	On the work of I. M. Vinogradov M. A. Korolev Internet video conference "Day of Mathematics and Mechanics" September 19, 2011 12:05
113.	On Gram's law in the theory of the Riemann zeta function M. Korolev International symposium "Arithmetic days in Moscow" June 13, 2011 16:30
114.	Закон Грама и аргумент дзета-функции Римана M. A. Korolev Moscow Seminar on the Number Theory April 8, 2011 18:30
115.	О законе Грама в теории дзета-функции Римана M. A. Korolev Seminar on Arithmetic Algebraic Geometry September 22, 2010 11:00
116.	Гипотеза Сельберга о нулях дзета-функции Римана и «закон Грама» M. A. Korolev Seminar on Arithmetic Algebraic Geometry November 26, 2009 15:00

Books in Math-Net.Ru

M. A. Korolev, Introduction to the sieve method, 2024, 64 с.
http://mi.mathnet.ru/book2014
Analytic and Combinatorial Number Theory, Collected papers. In commemoration of the 130th birth anniversary of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 314, ed. D. V. Treschev, S. V. Konyagin, V. N. Chubarikov, M. A. Korolev, M. R. Gabdullin, 2021, 346 с.
http://mi.mathnet.ru/book1847
Analytic number theory, On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba, Trudy Mat. Inst. Steklova, 299, ed. M. A. Korolev, A. G. Sergeev, 2017, 303 с.
http://mi.mathnet.ru/book1664
M. A. Korolev, Gram's Law in the Theory of Riemann Zeta-Function. Part 2, Sovrem. Probl. Mat., 21, 2016, 94 с.
http://mi.mathnet.ru/book1616
M. A. Korolev, Gram's Law in the Theory of Riemann Zeta-Function. Part 1, Sovrem. Probl. Mat., 20, 2015, 162 с.
http://mi.mathnet.ru/book1602

Organisations