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Bykovskii, Victor Alexeevich

Statistics Math-Net.Ru
Total publications: 54
Scientific articles: 48
Presentations: 7

Number of views:
This page:5971
Abstract pages:15922
Full texts:4944
References:1260
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.

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

Publications in Math-Net.Ru
2021
1. V. A. Bykovskii, M. A. Romanov, A. V. Ustinov, “Tropical sequences associated with Somos sequences”, Chebyshevskii Sb., 22:1 (2021),  118–132  mathnet
2. V. A. Bykovskii, M. A. Romanov, “Polynomial Somos Sequences”, Funktsional. Anal. i Prilozhen., 55:1 (2021),  20–32  mathnet; Funct. Anal. Appl., 55:1 (2021), 15–25  isi  scopus
2020
3. 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
4. V. A. Bykovskii, “Decomposition in terms of special functions”, Dal'nevost. Mat. Zh., 19:2 (2019),  138–172  mathnet
5. V. A. Bykovskii, “Extremal cubature formulas for anisotropic classes”, Dal'nevost. Mat. Zh., 19:1 (2019),  10–19  mathnet
6. 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
7. 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
2018
8. V. A. Bykovsky, “On one property of the Maass and Shintani functionals”, Chebyshevskii Sb., 19:3 (2018),  40–45  mathnet  elib
9. 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
10. V. A. Bykovskii, “Integer Somos-4 sequence with rational coefficients”, Dal'nevost. Mat. Zh., 18:2 (2018),  147–149  mathnet
11. V. A. Bykovskii, “On the Laurent property of the Somos-4 sequences”, Dal'nevost. Mat. Zh., 18:1 (2018),  18–22  mathnet
2017
12. V. A. Bykovskii, “Eichler – Shimura relations for theta functions”, Dal'nevost. Mat. Zh., 17:2 (2017),  152–157  mathnet  elib
13. V. A. Bykovskii, “On the distribution of integer points on a hyperboloid”, Dal'nevost. Mat. Zh., 17:2 (2017),  147–151  mathnet  elib
14. 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  elib; Izv. Math., 81:2 (2017), 239–268  isi  scopus
15. 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  elib; Sb. Math., 208:5 (2017), 644–683  isi  scopus
2016
16. M. O. Avdeeva, V. A. Bykovskii, “Hyperelliptic system of sequences and functions”, Dal'nevost. Mat. Zh., 16:2 (2016),  115–122  mathnet  elib
17. V. A. Bykovskii, “The Eisenstein-Hecke series and their properties”, Dal'nevost. Mat. Zh., 16:1 (2016),  3–8  mathnet  elib
18. 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
2015
19. 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
20. 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
21. V. A. Bykovskii, D. A. Frolenkov, “Some integral representations of hypergeometric function”, Dal'nevost. Mat. Zh., 15:1 (2015),  38–40  mathnet  elib
2014
22. V. A. Bykovskii, “On the distribution of integer points on the determinant surface”, Dal'nevost. Mat. Zh., 14:2 (2014),  156–159  mathnet
2013
23. 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
2012
24. 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
2011
25. 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
26. 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
2010
27. V. A. Bykovskii, “In the wake of the old past”, Dal'nevost. Mat. Zh., 10:1 (2010),  3–8  mathnet
28. 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
2009
29. V. A. Bykovskii, “Eichler – Shimura – Manin Theory”, Dal'nevost. Mat. Zh., 9:1-2 (2009),  29–37  mathnet  elib
30. 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
2008
31. 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
32. 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
33. 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
34. 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
2005
35. 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
2003
36. 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
37. 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
2001
38. 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
2000
39. 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
1999
40. 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
1996
41. 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
1994
42. 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
1991
43. 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
44. 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
45. 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
1987
46. V. A. Bykovskii, A. I. Vinogradov, “Nonhomogeneous convolutions”, Zap. Nauchn. Sem. LOMI, 160 (1987),  16–30  mathnet  zmath
1985
47. V. A. Bykovskii, “Arithmetic-analytical properties of binary positive definite quadratic forms”, Zap. Nauchn. Sem. LOMI, 144 (1985),  5–20  mathnet  mathscinet  zmath
1984
48. 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
1982
49. 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
50. 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
51. 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

2019
52. V. A. Bykovskii, “About scientific creativity of Askold Ivanovich Vinogradov”, Chebyshevskii Sb., 20:3 (2019),  22–26  mathnet
2016
53. 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
54. 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
55. 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
56. 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
57. 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

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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