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Bykovskii, Victor Alexeevich
Corresponding member of RAS
Professor
Doctor of physico-mathematical sciences (1993)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
Birth date: 5.09.1957
E-mail:
Keywords: analytic number theory, dynamical systems, continued fractions, Kloosterman sums, billiards, geometry of numbers, uniform distribution, Korobov lattice points, lattice, relative minimum.
UDC: 511.33, 511.334, 511.36, 511.37, 511.9, 515.178, 519.21, 512.754, 519.644.7, 511.292

Subject:

Analytic number theory, dynamical systems, continued fractions, Kloosterman sums, billiards, geometry of numbers.
   
Main publications:
  • V. A. Bykovskii. Otnositelnye minimumy reshetok i vershiny mnogogrannikov Kleina, Funkts. analiz i ego pril., 2006, 40:1, 69–71.
  • M. O. Avdeeva, V. A. Bykovskii. Utochnenie teoremy Valena dlya bazisov Minkovskogo trekhmernykh reshetok, Matem. zametki, 2006, 79:2, 163–168.
  • V. A. Bykovskii. Otsenka dispersii dlin konechnykh nepreryvnykh drobei, Fundament. i prikl. matem., 2005, 11:6, 15–26.
  • V. A. Bykovskii. Obrazuyuschie elementy annuliruyuschego ideala dlya modulyarnykh simvolov, Funkts. analiz i ego pril., 2003, 37:4, 27–38.
  • M. O. Avdeeva, V. A. Bykovskii. Analog teoremy Valena dlya sovmestnykh priblizhenii pary chisel, Matem. sb., 2003, 194:7, 3–14.
  • V. A. Bykovskii, O. A. Gorkusha. Minimalnye bazisy trekhmernykh polnykh reshetok, Matem. sb., 2001, 192:2, 57–66.
  • V. A. Bykovskii. Funktsionalnye uravneniya dlya ryadov Gekke–Maassa, Funkts. analiz i ego pril., 2000, 34:2, 23–32.
  • V. A. Bykovskii. Teorema Valena dlya dvumernykh podkhodyaschikh drobei, Matem. zametki, 1999, 66:1, 30–37.
  • V. A. Bykovskii. Diskretnoe preobrazovanie Fure i tsiklicheskaya svertka na tselochislennykh reshetkakh, Matem. sb., 1988, 136(178):4(8), 451–467.
  • V. A. Bykovskii, A. I. Vinogradov, O. V. Lokutsievskii, N. I. Feldman. Nikolai Mikhailovich Korobov (k semidesyatiletiyu so dnya rozhdeniya), UMN, 1988, 43:1(259), 221–222.

https://www.mathnet.ru/eng/person8740
List of publications on Google Scholar
https://mathscinet.ams.org/mathscinet/MRAuthorID/210711

Publications in Math-Net.Ru Citations
2023
1. V. A. Bykovskii, M. D. Monina, “Periodic ultradiscrete transformations of the space”, Dal'nevost. Mat. Zh., 23:1 (2023),  12–15  mathnet
2021
2. V. A. Bykovskii, M. A. Romanov, A. V. Ustinov, “Tropical sequences associated with Somos sequences”, Chebyshevskii Sb., 22:1 (2021),  118–132  mathnet 1
3. V. A. Bykovskii, “Periodic ultradiscrete plane transformations”, Dokl. RAN. Math. Inf. Proc. Upr., 500 (2021),  23–25  mathnet  zmath  elib; Dokl. Math., 104:2 (2021), 240–241  scopus 1
4. V. A. Bykovskii, M. A. Romanov, “Polynomial Somos Sequences”, Funktsional. Anal. i Prilozhen., 55:1 (2021),  20–32  mathnet  elib; Funct. Anal. Appl., 55:1 (2021), 15–25  isi  scopus 2
2020
5. V. A. Bykovskii, A. V. Ustinov, “Three-dimensional analogues of the Heath-Brown and Selberg identities”, Dokl. RAN. Math. Inf. Proc. Upr., 494 (2020),  14–16  mathnet  zmath  elib; Dokl. Math., 102:2 (2020), 364–366
6. V. A. Bykovskii, M. D. Monina, “Trace formula for integral points on the three-dimensional sphere”, Dokl. RAN. Math. Inf. Proc. Upr., 490 (2020),  13–15  mathnet  zmath  elib; Dokl. Math., 101:1 (2020), 9–11
7. V. A. Bykovskii, “Calculation of random pairs of primes whose product lies in a given short interval”, Dal'nevost. Mat. Zh., 20:2 (2020),  150–154  mathnet
2019
8. V. A. Bykovskii, “Decomposition in terms of special functions”, Dal'nevost. Mat. Zh., 19:2 (2019),  138–172  mathnet
9. V. A. Bykovskii, “Extremal cubature formulas for anisotropic classes”, Dal'nevost. Mat. Zh., 19:1 (2019),  10–19  mathnet 2
10. M. O. Avdeeva, V. A. Bykovskii, “On subsequences of even elements of Somos-6 sequenses”, Dal'nevost. Mat. Zh., 19:1 (2019),  3–5  mathnet
11. V. A. Bykovskii, A. V. Ustinov, “On the Laurent phenomenon for Somos-$4$ and Somos-$5$ sequences”, Funktsional. Anal. i Prilozhen., 53:3 (2019),  79–83  mathnet  mathscinet  elib 3
2018
12. V. A. Bykovsky, “On one property of the Maass and Shintani functionals”, Chebyshevskii Sb., 19:3 (2018),  40–45  mathnet  elib
13. V. A. Bykovskii, M. D. Monina, “Integer sequences Somos-4”, Dokl. Akad. Nauk, 481:5 (2018),  471–473  mathnet  zmath  elib; Dokl. Math., 98:1 (2018), 357–359  isi  scopus
14. V. A. Bykovskii, “Integer Somos-4 sequence with rational coefficients”, Dal'nevost. Mat. Zh., 18:2 (2018),  147–149  mathnet 1
15. V. A. Bykovskii, “On the Laurent property of the Somos-4 sequences”, Dal'nevost. Mat. Zh., 18:1 (2018),  18–22  mathnet 1
2017
16. V. A. Bykovskii, “Eichler – Shimura relations for theta functions”, Dal'nevost. Mat. Zh., 17:2 (2017),  152–157  mathnet  elib
17. V. A. Bykovskii, “On the distribution of integer points on a hyperboloid”, Dal'nevost. Mat. Zh., 17:2 (2017),  147–151  mathnet  elib
18. V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formulae for the second moments of $L$-series of holomorphic cusp forms on the critical line”, Izv. RAN. Ser. Mat., 81:2 (2017),  5–34  mathnet  mathscinet  zmath  elib; Izv. Math., 81:2 (2017), 239–268  isi  scopus 5
19. V. A. Bykovskii, D. A. Frolenkov, “The average length of finite continued fractions with fixed denominator”, Mat. Sb., 208:5 (2017),  63–102  mathnet  mathscinet  zmath  elib; Sb. Math., 208:5 (2017), 644–683  isi  scopus 2
2016
20. M. O. Avdeeva, V. A. Bykovskii, “Hyperelliptic system of sequences and functions”, Dal'nevost. Mat. Zh., 16:2 (2016),  115–122  mathnet  elib 10
21. V. A. Bykovskii, “The Eisenstein-Hecke series and their properties”, Dal'nevost. Mat. Zh., 16:1 (2016),  3–8  mathnet  elib
22. V. A. Bykovskii, “Hyperquasipolynomials and their applications”, Funktsional. Anal. i Prilozhen., 50:3 (2016),  34–46  mathnet  mathscinet  elib; Funct. Anal. Appl., 50:3 (2016), 193–203  isi  scopus 18
2015
23. V. A. Bykovskii, D. A. Frolenkov, “Asymptotic formula for the convolution of a generalized divisor function”, Dokl. Akad. Nauk, 465:2 (2015),  137–140  mathnet  elib; Dokl. Math., 92:3 (2015), 670–673  isi  scopus 1
24. V. A. Bykovskii, D. A. Frolenkov, “On the second moment of $L$-series of holomorphic cusp forms on the critical line”, Dokl. Akad. Nauk, 463:2 (2015),  133–136  mathnet  mathscinet  zmath  elib; Dokl. Math., 92:1 (2015), 417–420  isi  scopus 5
25. V. A. Bykovskii, D. A. Frolenkov, “Some integral representations of hypergeometric function”, Dal'nevost. Mat. Zh., 15:1 (2015),  38–40  mathnet  elib 1
2014
26. V. A. Bykovskii, “On the distribution of integer points on the determinant surface”, Dal'nevost. Mat. Zh., 14:2 (2014),  156–159  mathnet 1
2013
27. V. A. Bykovskii, M. D. Monina, “On the arithmetic nature of some identities of the elliptic functions theory”, Dal'nevost. Mat. Zh., 13:1 (2013),  15–34  mathnet 4
2012
28. V. A. Bykovskii, “The discrepancy of the Korobov lattice points”, Izv. RAN. Ser. Mat., 76:3 (2012),  19–38  mathnet  mathscinet  zmath  elib; Izv. Math., 76:3 (2012), 446–465  isi  elib  scopus 17
2011
29. N. V. Budarina, V. A. Bykovskii, “The arithmetic nature of the triple and quintuple product identities”, Dal'nevost. Mat. Zh., 11:2 (2011),  140–148  mathnet 6
30. V. A. Bykovskii, S. V. Gassan, “Optimality parameter of Korobov parallelepipedal grids for cubature formulas”, Zh. Vychisl. Mat. Mat. Fiz., 51:8 (2011),  1363–1369  mathnet  mathscinet; Comput. Math. Math. Phys., 51:8 (2011), 1273–1279  isi  scopus 1
2010
31. V. A. Bykovskii, “In the wake of the old past”, Dal'nevost. Mat. Zh., 10:1 (2010),  3–8  mathnet
32. M. O. Avdeeva, V. A. Bykovskii, “Upper and Lower Bounds for the Voronoi–Minkowski constant”, Mat. Zametki, 87:4 (2010),  483–491  mathnet  mathscinet  zmath; Math. Notes, 87:4 (2010), 457–465  isi  scopus 2
2009
33. V. A. Bykovskii, “Eichler – Shimura – Manin Theory”, Dal'nevost. Mat. Zh., 9:1-2 (2009),  29–37  mathnet  elib
34. V. A. Bykovskii, A. V. Ustinov, “The statistics of particle trajectories in the inhomogeneous Sinai problem for a two-dimensional lattice”, Izv. RAN. Ser. Mat., 73:4 (2009),  17–36  mathnet  mathscinet  zmath  elib; Izv. Math., 73:4 (2009), 669–688  isi  elib  scopus 14
2008
35. V. A. Bykovskii, A. V. Ustinov, “The Statistics of Particle Trajectories in the Homogeneous Sinai Problem for a Two-Dimensional Lattice”, Funktsional. Anal. i Prilozhen., 42:3 (2008),  10–22  mathnet  mathscinet  zmath; Funct. Anal. Appl., 42:3 (2008), 169–179  isi  scopus 6
36. V. A. Bykovskii, “On the distribution of prime denominators of the approximants for almost all real numbers”, Izv. RAN. Ser. Mat., 72:2 (2008),  65–82  mathnet  mathscinet  zmath  elib; Izv. Math., 72:2 (2008), 265–282  isi  elib  scopus
2006
37. V. A. Bykovskii, “Local Minima of Lattices and Vertices of Klein Polyhedra”, Funktsional. Anal. i Prilozhen., 40:1 (2006),  69–71  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 40:1 (2006), 56–57  isi  scopus 8
38. M. O. Avdeeva, V. A. Bykovskii, “Refinement of Vahlen's Theorem for Minkowski Bases of Three-Dimensional Lattices”, Mat. Zametki, 79:2 (2006),  163–168  mathnet  mathscinet  zmath  elib; Math. Notes, 79:2 (2006), 151–156  isi  elib  scopus 4
2005
39. V. A. Bykovskii, “Estimate for dispersion of lengths of continued fractions”, Fundam. Prikl. Mat., 11:6 (2005),  15–26  mathnet  mathscinet  zmath; J. Math. Sci., 146:2 (2007), 5634–5643  scopus 10
2003
40. V. A. Bykovskii, “Generating Elements of the Annihilating Ideal for Modular Symbols”, Funktsional. Anal. i Prilozhen., 37:4 (2003),  27–38  mathnet  mathscinet  zmath  elib; Funct. Anal. Appl., 37:4 (2003), 263–272  isi  scopus 8
41. M. O. Avdeeva, V. A. Bykovskii, “An analogue of Vahlen's theorem for simultaneous approximations of a pair of numbers”, Mat. Sb., 194:7 (2003),  3–14  mathnet  mathscinet  zmath; Sb. Math., 194:7 (2003), 955–967  isi  scopus 5
2001
42. V. A. Bykovskii, O. A. Gorkusha, “Minimal bases of three-dimensional complete lattices”, Mat. Sb., 192:2 (2001),  57–66  mathnet  mathscinet  zmath; Sb. Math., 192:2 (2001), 215–223  isi  scopus 8
2000
43. V. A. Bykovskii, “Functional Equations for Hecke–Maass Series”, Funktsional. Anal. i Prilozhen., 34:2 (2000),  23–32  mathnet  mathscinet  zmath; Funct. Anal. Appl., 34:2 (2000), 98–105  isi 6
1999
44. V. A. Bykovskii, “Vahlen theorem for two-dimensional convergents”, Mat. Zametki, 66:1 (1999),  30–37  mathnet  mathscinet  zmath; Math. Notes, 66:1 (1999), 24–29  isi 11
1996
45. V. A. Bykovskii, “A trace formula for convolution of Hecke series and its applications”, Zap. Nauchn. Sem. POMI, 226 (1996),  14–36  mathnet  mathscinet  zmath; J. Math. Sci. (New York), 89:1 (1998), 915–932 33
1994
46. V. A. Bykovskii, “Density theorems and the mean value of arithmetical functions in short intervals”, Zap. Nauchn. Sem. POMI, 212 (1994),  56–70  mathnet  mathscinet  zmath; J. Math. Sci., 83:6 (1997), 720–730 14
1991
47. V. A. Bykovskii, A. I. Vinogradov, “Mean value of Hecke series of parabolic forms”, Trudy Mat. Inst. Steklov., 200 (1991),  57–74  mathnet  mathscinet  zmath; Proc. Steklov Inst. Math., 200 (1993), 61–81
1988
48. V. A. Bykovskii, “Discrete Fourier transform and cyclic convolution on integral lattices”, Dokl. Akad. Nauk SSSR, 302:1 (1988),  11–13  mathnet  mathscinet  zmath; Dokl. Math., 38:2 (1989), 237–239 2
49. V. A. Bykovskii, “The discrete Fourier transform and cyclic convolution on integral lattices”, Mat. Sb. (N.S.), 136(178):4(8) (1988),  451–467  mathnet  mathscinet  zmath; Math. USSR-Sb., 64:2 (1989), 443–460 4
1987
50. V. A. Bykovskii, A. I. Vinogradov, “Nonhomogeneous convolutions”, Zap. Nauchn. Sem. LOMI, 160 (1987),  16–30  mathnet  zmath 1
1985
51. V. A. Bykovskii, “Arithmetic-analytical properties of binary positive definite quadratic forms”, Zap. Nauchn. Sem. LOMI, 144 (1985),  5–20  mathnet  mathscinet  zmath
1984
52. V. A. Bykovskii, “Spectral expansion of certain automorphic functions and its number-theoretical applications”, Zap. Nauchn. Sem. LOMI, 134 (1984),  15–33  mathnet  mathscinet  zmath 1
1982
53. V. A. Bykovskii, “On a summation formula in the spectral theory of automorphic functions and its applications in analytic number theory”, Dokl. Akad. Nauk SSSR, 264:2 (1982),  275–277  mathnet  mathscinet  zmath
1981
54. V. A. Bykovskii, “Asymptotic properties of integral points $(a_1,a_2)$, satisfying the congruence $a_1a_2\equiv l(q)$”, Zap. Nauchn. Sem. LOMI, 112 (1981),  5–25  mathnet  mathscinet  zmath; J. Soviet Math., 25:2 (1984), 975–988 9
55. V. A. Bykovskii, “System of inequalities”, Zap. Nauchn. Sem. LOMI, 109 (1981),  3–33  mathnet  mathscinet  zmath; J. Soviet Math., 24:2 (1984), 159–178 3
2024
56. V. M. Buchstaber, V. P. Platonov, A. L. Semenov, V. A. Bykovskii, Yu. V. Nesterenko, V. N. Chubarikov, N. M. Dobrovol'skii, “Sergei Petrovich Novikov (20.03.1938 – 6.06.2024)”, Chebyshevskii Sb., 25:2 (2024),  364–365  mathnet
57. Yu. V. Nesterenko, V. A. Bykovskii, V. N. Chubarikov, V. G. Chirskii, O. N. German, N. M. Dobrovol'skii, “Alexander Ivanovich Galochkin (on the 80-th anniversary of his birth)”, Chebyshevskii Sb., 25:2 (2024),  20–28  mathnet
2022
58. A. I. Shafarevich, A. T. Fomenko, V. N. Chubarikov, A. O. Ivanov, V. G. Chirskii, V. I. Bernik, V. A. Bykovskii, A. I. Galochkin, S. S. Demidov, S. B. Gashkov, A. I. Nizhnikov, A. A. Fomin, E. Deza, A. Ya. Kanel-Belov, N. M. Dobrovolsky, N. N. Dobrovolsky, I. Yu. Rebrova, V. Kh. Salikhov, “Yuri Valentinovich Nesterenko (to the 75th anniversary)”, Chebyshevskii Sb., 23:1 (2022),  10–20  mathnet
59. Yu. V. Nesterenko, V. A. Bykovskii, V. M. Bukhshtaber, V. G. Chirskii, V. N. Chubarikov, A. P. Laurinčikas, N. M. Dobrovol'skii, N. N. Dobrovol'skii, I. Yu. Rebrova, N. V. Budarina, V. V. Beresnevich, D. V. Vasilyev, N. I. Kalosha, “Vasily Ivanovich Bernik (to the 75th anniversary)”, Chebyshevskii Sb., 23:1 (2022),  6–9  mathnet
2019
60. V. A. Bykovskii, “About scientific creativity of Askold Ivanovich Vinogradov”, Chebyshevskii Sb., 20:3 (2019),  22–26  mathnet
2016
61. V. I. Bernik, V. A. Bykovskij, A. I. Galochkin, N. M. Dobrovol'skij, A. V. Zhmuljova, V. H. Salihov, V. G. Chirskij, V. N. Chubarikov, “Nesterenko Yuri Valentinovich (70 anniversary of Yu. V. Nesterenko)”, Chebyshevskii Sb., 17:4 (2016),  211–2210  mathnet  elib
62. Yu. V. Nesterenko, V. A. Bykovskii, V. M. Buchstaber, V. G. Chirsky, V. N. Chubarikov, A. Laurinchikas, N. M. Dobrovolsky, N. V. Budarina, I. V. Gaishun, V. V. Beresnevich, D. V. Vasiliev, “Vasily Ivanovich Bernik (on his seventieth)”, Chebyshevskii Sb., 17:4 (2016),  203–210  mathnet  elib
63. V. A. Bykovsky, N. M. Dobrovolsky, A. V. Zhmuleva, V. G. Chirskii, V. N. Chubarikov, “To 65-anniversary of the birth of Dmitry Alekseevich Mitkin (25.04.1951–09.04.2007)”, Chebyshevskii Sb., 17:2 (2016),  214–223  mathnet  elib
64. A. V. Parusnikova, O. S. Ogneva, V. A. Bykovskii, A. A. Vedenov, D. O. Golovin, Yu. O. Golovin, V. M. Zaitsev, B. K. Zuev, E. Yu. Zueva, K. M. Efimov, A. V. Ivanov, V. S. Isaev, A. S. Karyagina, A. L. Kolosov, S. P. Konovalov, P. A. Kornilov, V. V. Lavrov, V. A. Lavrova, A. A. Letunov, I. E. Letunova, V. D. Maiorov, A. B. Merkov, Yu. I. Ozhigov, S. Yu. Orevkov, O. A. Presnyakova, D. V. Reut, A. V. Skaraev, V. N. Sorokin, P. N. Sorokin, P. G. Sushilin, E. V. Fokina, N. N. Chentsova, T. I. Shvarts, A. S. Zibrov, S. V. Liskina, T. F. Nikiforova, E. G. Orevkova, M. L. Shvarts, “V. I. Parusnikov. Obituary”, Chebyshevskii Sb., 17:1 (2016),  284–285  mathnet  elib
1988
65. V. A. Bykovskii, A. I. Vinogradov, O. V. Lokutsievskii, N. I. Fel'dman, “Nikolai Mikhailovich Korobov (on his seventieth birthday)”, Uspekhi Mat. Nauk, 43:1(259) (1988),  221–222  mathnet  mathscinet; Russian Math. Surveys, 43:1 (1988), 265–267  isi 1

Presentations in Math-Net.Ru
1. Арифметические формулы следа
V. A. Bykovskii
Number Theory irregular seminar
February 27, 2020 16:00
2. Формула следа для целых точек на трехмерной сфере
V. A. Bykovskii
Number Theory irregular seminar
November 12, 2019 18:00
3. Задача Хоули о представлении натурального числа суммой квадрата и произведения
V. A. Bykovskii
Contemporary Problems in Number Theory
April 19, 2019 13:30
4. Spectral representations of Zeta functions of one-class imaginary quadratic fields
V. A. Bykovskii
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 28, 2018 13:10
5. The distribution of lattice points on the hyperboloid
V. A. Bykovskii
А.A.Karatsuba's 80th Birthday Conference in Number Theory and Applications
May 22, 2017 16:55   
6. Гиперквазимногочлены и их приложения
V. A. Bykovskii
Algebraic topology and its applications. Postnikov memorial seminar
December 22, 2015 16:45
7. Дискретные обмотки тора и приложения
V. A. Bykovskii
Meetings of the Moscow Mathematical Society
December 24, 2013 18:30

Organisations
 
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