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 and Selberg's conjecture on the distribution of zeros of the Riemann zeta function”, Izv. Math., 74:4 (2010), 743–780
5.
M. A. Korolev, “Short Kloosterman Sums with Weights”, Math. Notes, 88:3 (2010), 374–385
6.
M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158
7.
M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659
8.
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
9.
M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827
10.
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
11.
M. A. Korolev, “On large values of the function $S(t)$ on short intervals”, Izv. Math., 69:1 (2005), 113–122
12.
M. A. Korolev, “On Gram's law in the theory of the Riemann zeta function”, Izv. Math., 76:2 (2012), 275–309
13.
M. A. Korolev, “The argument of the Riemann zeta-function on the critical line”, Izv. Math., 67:2 (2003), 225–264
14.
M. A. Korolev, “Generalized Kloosterman sum with primes”, Proc. Steklov Inst. Math., 296 (2017), 154–171
15.
S. V. Konyagin, M. A. Korolev, “On a symmetric diophantine equation with reciprocals”, Proc. Steklov Inst. Math., 294 (2016), 67–77
16.
M. A. Korolev, “On the integral of Hardy's function $Z(t)$”, Izv. Math., 72:3 (2008), 429–478
17.
Maxim Korolev, Igor Shparlinski, “Sums of algebraic trace functions twisted by arithmetic functions”, Pacific J. Math., 304:2 (2020), 505–522 , arXiv: 1804.01337;
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, “Methods of estimating of incomplete Kloosterman sums”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 230–245
22.
M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661
23.
S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Sb. Math., 208:12 (2017), 1818–1834
24.
M. A. Korolev, “On non-linear Kloosterman sum”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 246–249
25.
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
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
M. A. Korolev, “On multiple zeros of the Riemann zeta function”, Izv. Math., 70:3 (2006), 427–446
28.
M. A. Korolev, “Sign changes of the function $S(t)$ on short intervals”, Izv. Math., 69:4 (2005), 719–731
29.
M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142
30.
M. A. Korolev, “On Incomplete Gaussian Sums”, Proc. Steklov Inst. Math., 290 (2015), 52–62
31.
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
32.
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;
M. A. Korolev, “Short Kloosterman Sums with Primes”, Math. Notes, 106:1 (2019), 89–97
35.
M. A. Korolev, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Math. Notes, 103:5 (2018), 761–768
36.
M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170
37.
M. A. Korolev, “On small values of the Riemann zeta-function at Gram points”, Sb. Math., 205:1 (2014), 63–82
38.
M. A. Korolev, “On new results related to Gram's law”, Izv. Math., 77:5 (2013), 917–940
39.
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
M. A. Korolev, “On the average number of power residues modulo a composite number”, Izv. Math., 74:6 (2010), 1225–1254
44.
M. A. Korolev, “On large distances between consecutive zeros of the Riemann zeta-function”, Izv. Math., 72:2 (2008), 291–304
45.
M. A. Korolev, D. A. Popov, “On Jutila's integral in the circle problem”, Izv. Math., 86:3 (2022), 413–455
46.
K. Gong, C. Jia, M.A. Korolev, “Shifted character sums with multiplicative coefficients, II”, J. Number Theory, 178 (2017), 31–39 , arXiv: 1611.06577v1
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
51.
M. A. Korolev, “Vinogradov's sieve and an estimate for an incomplete Kloosterman sum”, Sb. Math., 213:2 (2022), 216–234
52.
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)
53.
M. A. Korolev, M. E. Changa, “New Estimate for Kloosterman Sums with Primes”, Math. Notes, 108:1 (2020), 87–93
54.
Maxim A. Korolev, “Kloosterman sums over primes of composite moduli”, Res. Number Theory, 6 (2020), 24 , 20 pp. ;
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;
M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43
57.
M. A. Korolev, “Large values of the Riemann zeta-function on short intervals of the critical line”, Dokl. Math., 91:1 (2015), 102–104
58.
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
59.
M. A. Korolev, “On large distances between neighboring zeros of the Riemann zeta function”, Dokl. Math., 76:3 (2007), 940–943
60.
A. A. Karatsuba, M. A. Korolëv, “Priblizhenie trigonometricheskoi summy bolee korotkoi”, Dokl. RAN, 412:2 (2007), 159–161
M. A. Korolev, “On the period of the continued fraction expansion for $\sqrt{d}$”, Izv. RAN. Ser. Mat. (to appear)
62.
M. A. Korolev, “The structures generated on the unit circle by residues to given modulus”, Mat. Zametki, 116:5 (2024), 766–791 (to appear)
63.
Maxim Korolev, Antanas Laurinčikas, “Joint functional independence of the Riemann zeta-function”, Indian J. Pure Appl. Math., 2024, 1–6 (Published online) ; (Published online)
64.
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
65.
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, 8–11http://poivs.tsput.ru/conf/international/XXII/files/Conference2023S.pdf?v=3
66.
M. A. Korolev, “A distribution related to Farey series”, Chebyshevskii Sb., 24:4 (2023), 137–190
67.
M. A. Korolev, I. S. Rezvyakova, “O sovmestnykh priblizheniyakh logarifmov prostykh chisel”, Chebyshevskii sb., 23:5 (2022), 87–100
M. A. Korolev, “Kloosterman Sums with Primes and Solvability of a Congruence with Inverse Residues”, Proc. Steklov Inst. Math., 314 (2021), 96–126
70.
A. T. Daniyarkhodzhaev, M. A. Korolev, “On a Ramanujan Identity and Its Generalizations”, Math. Notes, 110:4 (2021), 511–521
71.
M. A. Korolev, I. S. Rezvyakova, “Incomplete Kloosterman sums to prime power modules”, Bull., Cl. Sci. Math. Nat., Sci. Math., 46 (2021), 73–92;
72.
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. ;
73.
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
74.
V. M. Buchstaber, M. A. Korolev, “On the scientific works of Dmitry Alexandrovich Popov”, Chebyshevskii Sb., 21:4 (2020), 396–421
75.
M. A. Korolev, A. V. Ustinov, “Distribution of rational points on the circle of unit radius”, Izv. Math., 83:5 (2019), 1008–1049
76.
M. A. Korolev, Kloosterman sums with primes to composite moduli, 2019 , 23 pp., arXiv: 1911.09981
77.
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
78.
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
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
81.
M. A. Korolev, A. V. Ustinov, “The Distribution of the Rational Points on the Unit Circle”, Dokl. Math., 98:1 (2018), 321–324
82.
M. A. Korolev, I. E. Shparlinski, Sums of algebraic trace functions twisted by arithmetic functions, 2018 , 19 pp., arXiv: 1804.01337
83.
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
84.
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
85.
M. A. Korolev, “The estimate of weighted Kloosterman sums by additive shift”, Doklady Mathematics (Supplementary issues), 106:2 (2022), 221–229
86.
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
87.
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
88.
M. A. Korolev, On Kloosterman sums with multiplicative coefficients, 2016 , 13 pp., arXiv: 1610.09171
89.
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
90.
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
91.
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
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
94.
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)
95.
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
96.
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, 24–26http://mjcnt.phystech.edu/conference/palanga/abstract_book.pdf (Supported by Yandex, Vilnius University and Moscow Journal of Combinatorics and Number Theory)
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
99.
M. A. Korolev, “On some new results related to Gram's law”, Dokl. Math., 86:2 (2012), 661–662
100.
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
101.
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
102.
M. A. Korolev, “On the primitive of the Hardy function $Z(t)$”, Dokl. Math., 75:2 (2007), 295–298
103.
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
104.
M. A. Korolev, “On a new multiplicative function”, Russian Math. Surveys, 53:4 (1998), 868–869
105.
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
106.
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
107.
M. A. Korolev, Vvedenie v metod resheta, Letnyaya shkola “Sovremennaya matematika”, MTsNMO, Moskva, 2024 , 56 pp.
108.
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
109.
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
110.
M. A. Korolev, “Udivlyayuschaya prostota. O dostizheniyakh Dzheimsa Meinarda”, Troitskii variant, 2022, no. 14 (358), 26 iyulya 2022 g., 7http://trv-science.ru/uploads/358N.pdf
111.
M. Korolev, Kvant, 2021, no. 8, 2–9
112.
T. G. Bobkina, M. A. Korolev, “K 130-letiyu I.M. Vinogradova”, Kvant, 2021, no. 9, 13–15
113.
M. A. Korolev, “Obmanchivaya prostota prostykh chisel”, Kvant, 2020, no. 3, 10–17
114.
M. A. Korolev, “Letter to the editors”, Izv. Math., 75:4 (2011), 869
115.
M. A. Korolëv, “Sodokladchiki”, My – matematiki s Leninskikh gor, Vypusk № 5 «V. I. Arnold», Moskva, 2011, 312
116.
M. A. Korolev, “Esche raz o posledovatelnostyakh Rachinskogo”, Nauka i zhizn, 2007, no. 10, 89–91 (http://www.nkj.ru/archive/articles/11844/)
117.
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.
118.
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.
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
6.
Дизайны на окружности Максим Королёв Mathematical seminar Faculty of Computer Science HSE March 1, 2024 18:10
7.
Дизайны на окружности M. A. Korolev Contemporary Problems in Number Theory February 29, 2024 12:45
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
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
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
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
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
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
Contact us: