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Ustinov, Alexey Vladimirovich
Statistics Math-Net.Ru
Total publications: 64
Scientific articles: 54
Presentations: 23

Number of views:
This page:11305
Abstract pages:30615
Full texts:15093
References:2832
Ustinov, Alexey Vladimirovich
Professor of Russian Academy of Sciences
Associate professor
Doctor of physico-mathematical sciences (2009)
Speciality: 01.01.06 (Mathematical logic, algebra, and number theory)
E-mail:
Website: https://www.hse.ru/en/org/persons/530309935
Keywords: analytic number theory, continued fractions, Kloosterman sums, geometry of numbers.
UDC: 511.218, 511.33, 511.335, 511.336, 511.37, 511.51, 519.68, 517.524, 519.21, 510.52, 519.712.61, 511.512, 511.528, 514.174.6

Subject:

Analytic number theory
   
Main publications:
  1. M. B. Skopenkov, A. V. Ustinov, “Feynman checkers: towards algorithmic quantum theory”, Uspekhi Mat. Nauk, 77:3(465) (2022), 73–160  mathnet  crossref; Russian Math. Surveys, 77:3 (2022), 445–530  crossref
  2. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Uspekhi Mat. Nauk, 70:3(423) (2015), 107–180  mathnet  crossref  mathscinet  zmath  adsnasa  elib; Russian Math. Surveys, 70:3 (2015), 483–556  crossref  isi  scopus
  3. A. V. Ustinov, “Spin chains and Arnolds problem on the Gauss-Kuzmin statistics for quadratic irrationals”, Mat. Sb., 204:5 (2013), 143–160  mathnet  crossref  mathscinet  zmath  adsnasa  elib; Sb. Math., 204:5 (2013), 762–779  crossref  isi  elib  scopus
  4. V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of formal group laws”, Mat. Sb., 206:11 (2015), 19–60  mathnet  crossref  mathscinet  adsnasa  elib; Sb. Math., 206:11 (2015), 1524–1563  crossref  isi  scopus
  5. A. V. Ustinov, “On the distribution of Frobenius numbers with three arguments”, Izv. RAN. Ser. Mat., 74:5 (2010), 145–170  mathnet  crossref  mathscinet  zmath  adsnasa  elib; Izv. Math., 74:5 (2010), 1023–1049  crossref  isi  elib  scopus

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Publications in Math-Net.Ru Citations
2024
1. A. V. Ustinov, “On Periodicity of the Somos Sequences Modulo $m$”, Mat. Zametki, 115:3 (2024),  439–449  mathnet  mathscinet; Math. Notes, 115:3 (2024), 405–413  scopus
2022
2. A. V. Ustinov, “A Short Proof of the Landsberg–Schaar Identity”, Mat. Zametki, 112:3 (2022),  478–480  mathnet  mathscinet; Math. Notes, 112:3 (2022), 488–490  scopus
3. M. B. Skopenkov, A. V. Ustinov, “Feynman checkers: towards algorithmic quantum theory”, Uspekhi Mat. Nauk, 77:3(465) (2022),  73–160  mathnet  mathscinet; Russian Math. Surveys, 77:3 (2022), 445–530  isi  scopus 6
2021
4. V. A. Bykovskii, M. A. Romanov, A. V. Ustinov, “Tropical sequences associated with Somos sequences”, Chebyshevskii Sb., 22:1 (2021),  118–132  mathnet 1
5. A. V. Ustinov, “On Somos-4 and Somos-5 Sequences”, Mat. Zametki, 110:3 (2021),  478–480  mathnet  elib; Math. Notes, 110:3 (2021), 470–472  isi  scopus 1
2020
6. 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
2019
7. A. V. Ustinov, “A simplified proof of Ward's formula for elliptic sequences”, Dal'nevost. Mat. Zh., 19:1 (2019),  84–87  mathnet
8. 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
9. M. A. Korolev, A. V. Ustinov, “Distribution of rational points on the circle of unit radius”, Izv. RAN. Ser. Mat., 83:5 (2019),  107–148  mathnet  mathscinet  elib; Izv. Math., 83:5 (2019), 1008–1049  isi  scopus
10. A. V. Ustinov, “On Formal Buchstaber Groups of Special Form”, Mat. Zametki, 105:6 (2019),  899–910  mathnet  mathscinet  elib; Math. Notes, 105:6 (2019), 894–904  isi  scopus 1
11. I. S. Vorob'ev, A. V. Ustinov, “Symmetric semigroups with three generators”, Mat. Sb., 210:12 (2019),  31–42  mathnet  mathscinet  elib; Sb. Math., 210:12 (2019), 1690–1701  isi  scopus
12. A. V. Ustinov, “An Elementary Approach to the Study of Somos Sequences”, Trudy Mat. Inst. Steklova, 305 (2019),  330–343  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 305 (2019), 305–317  isi  scopus 5
2018
13. M. A. Korolev, A. V. Ustinov, “The Distribution of the Rational Points on the Unit Circle”, Dokl. Akad. Nauk, 481:2 (2018),  131–135  mathnet  elib; Dokl. Math., 98:1 (2018), 321–324  isi  elib  scopus
2017
14. A. V. Ustinov, “Buchstaber Formal Group and Elliptic Functions of Small Levels”, Mat. Zametki, 102:1 (2017),  96–108  mathnet  mathscinet  elib; Math. Notes, 102:1 (2017), 81–91  isi  scopus 2
2016
15. M. A. Guzev, A. V. Ustinov, “Mechanical characteristics of molecular dynamics model and Korobov polynomials”, Dal'nevost. Mat. Zh., 16:1 (2016),  39–43  mathnet  elib 2
16. E. Yu. Bunkova, V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of Tate formal groups determining Krichever genera”, Trudy Mat. Inst. Steklova, 292 (2016),  43–68  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 292 (2016), 37–62  isi  elib  scopus 6
2015
17. V. I. Bernik, A. G. Gusakova, A. V. Ustinov, “Distribution of algebraic points in domains of small measure and near the surfaces”, Chebyshevskii Sb., 16:3 (2015),  78–94  mathnet  elib
18. A. V. Ustinov, “On Points of the Modular Hyperbola under the Graph of a Linear Function”, Mat. Zametki, 97:2 (2015),  296–301  mathnet  mathscinet  zmath  elib; Math. Notes, 97:2 (2015), 284–288  isi  scopus 4
19. A. V. Ustinov, “On a Generalization of Kloosterman Sums”, Mat. Zametki, 97:1 (2015),  154–157  mathnet  mathscinet  zmath  elib; Math. Notes, 97:1 (2015), 147–151  isi  scopus 2
20. A. V. Ustinov, “Three-dimensional continued fractions and Kloosterman sums”, Uspekhi Mat. Nauk, 70:3(423) (2015),  107–180  mathnet  mathscinet  zmath  elib; Russian Math. Surveys, 70:3 (2015), 483–556  isi  scopus 3
21. V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of formal group laws”, Mat. Sb., 206:11 (2015),  19–60  mathnet  mathscinet  elib; Sb. Math., 206:11 (2015), 1524–1563  isi  scopus 12
22. A. V. Ustinov, “The distribution of solutions of a determinantal equation”, Mat. Sb., 206:7 (2015),  103–134  mathnet  mathscinet  zmath  elib; Sb. Math., 206:7 (2015), 988–1019  isi  scopus 1
2014
23. V. I. Bernik, A. V. Ustinov, “On the distribution of points on the modular hyperbola”, Dal'nevost. Mat. Zh., 14:2 (2014),  141–155  mathnet 2
24. A. V. Ustinov, “On continued fractions of equal length”, Dal'nevost. Mat. Zh., 14:1 (2014),  96–99  mathnet
25. A. V. Ustinov, “Calculation of a Gauss sum via the discrete Fourier transform”, Dal'nevost. Mat. Zh., 14:1 (2014),  90–95  mathnet 1
26. M. B. Skopenkov, A. A. Pakharev, A. V. Ustinov, “Сквозь сеть сопротивлений”, Mat. Pros., Ser. 3, 18 (2014),  33–65  mathnet 1
27. A. V. Ustinov, “On the Three-Dimensional Vahlen Theorem”, Mat. Zametki, 95:1 (2014),  154–156  mathnet  mathscinet  zmath  elib; Math. Notes, 95:1 (2014), 136–138  isi  elib  scopus 3
2013
28. A. V. Ustinov, “Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals”, Mat. Sb., 204:5 (2013),  143–160  mathnet  mathscinet  zmath  elib; Sb. Math., 204:5 (2013), 762–779  isi  elib  scopus 7
2012
29. M. Skopenkov, V. Smykalov, A. V. Ustinov, “Случайные блуждания и электрические цепи”, Mat. Pros., Ser. 3, 16 (2012),  25–47  mathnet
30. A. V. Ustinov, “Minimal Vector Systems in 3-Dimensional Lattices and Analog of Vahlen's Theorem for 3-Dimensional Minkowski's Continued Fractions”, Sovrem. Probl. Mat., 16 (2012),  103–128  mathnet  zmath  elib; Proc. Steklov Inst. Math., 280, suppl. 2 (2013), S91–S116  isi  scopus 4
31. A. V. Ustinov, “Geometric proof of Rødseth's formula for Frobenius numbers”, Trudy Mat. Inst. Steklova, 276 (2012),  280–287  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 276 (2012), 275–282  isi  elib  scopus 5
2011
32. A. V. Ustinov, “On Voronoi's cylindric minima theorem”, Dal'nevost. Mat. Zh., 11:2 (2011),  213–221  mathnet 1
33. A. V. Ustinov, “On Gauss — Kuz'min statistics in short intervals”, Dal'nevost. Mat. Zh., 11:1 (2011),  93–98  mathnet 3
34. D. Baranov, M. Skopenkov, A. Ustinov, “Сопротивление между узлами решетки”, Mat. Pros., Ser. 3, 15 (2011),  229–230  mathnet
2010
35. A. V. Ustinov, “On the distribution of Frobenius numbers with three arguments”, Izv. RAN. Ser. Mat., 74:5 (2010),  145–170  mathnet  mathscinet  zmath  elib; Izv. Math., 74:5 (2010), 1023–1049  isi  elib  scopus 16
36. A. V. Ustinov, “The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients”, Mat. Zametki, 88:4 (2010),  594–604  mathnet  mathscinet; Math. Notes, 88:4 (2010), 574–584  isi  scopus 8
2009
37. A. V. Ustinov, “On the statistical properties of elements of continued fractions”, Dokl. Akad. Nauk, 424:4 (2009),  459–461  mathnet  mathscinet  elib; Dokl. Math., 79:1 (2009), 87–89  isi  elib  scopus 7
38. A. V. Ustinov, “On the distribution of integer points”, Dal'nevost. Mat. Zh., 9:1-2 (2009),  176–181  mathnet  elib 5
39. 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
40. A. V. Ustinov, “The Mean Number of Steps in the Euclidean Algorithm with Least Absolute-Value Remainders”, Mat. Zametki, 85:1 (2009),  153–156  mathnet  mathscinet  zmath  elib; Math. Notes, 85:1 (2009), 142–145  isi  scopus 9
41. A. V. Ustinov, “The solution of Arnold's problem on the weak asymptotics of Frobenius numbers with three arguments”, Mat. Sb., 200:4 (2009),  131–160  mathnet  mathscinet  zmath  elib; Sb. Math., 200:4 (2009), 597–627  isi  elib  scopus 20
2008
42. A. V. Ustinov, “On the number of solutions of the congruence $xy\equiv l$ $(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function”, Algebra i Analiz, 20:5 (2008),  186–216  mathnet  mathscinet  zmath  elib; St. Petersburg Math. J., 20:5 (2009), 813–836  isi 30
43. 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
44. A. V. Ustinov, “Asymptotic behaviour of the first and second moments for the number of steps in the Euclidean algorithm”, Izv. RAN. Ser. Mat., 72:5 (2008),  189–224  mathnet  mathscinet  zmath  elib; Izv. Math., 72:5 (2008), 1023–1059  isi  elib  scopus 12
2007
45. A. V. Ustinov, “Calculation of the variance in a problem in the theory of continued fractions”, Mat. Sb., 198:6 (2007),  139–158  mathnet  mathscinet  zmath  elib; Sb. Math., 198:6 (2007), 887–907  isi  elib  scopus 6
2006
46. A. V. Ustinov, “A Short Proof of Euler's Identity for Continuants”, Mat. Zametki, 79:1 (2006),  155–156  mathnet  mathscinet  zmath  elib; Math. Notes, 79:1 (2006), 146–147  isi  scopus 6
2005
47. A. V. Ustinov, “On Gauss–Kuz'min statistics for finite continued fractions”, Fundam. Prikl. Mat., 11:6 (2005),  195–208  mathnet  mathscinet  zmath; J. Math. Sci., 146:2 (2007), 5771–5781  scopus 5
48. A. V. Ustinov, “On the statistical properties of finite continued fractions”, Zap. Nauchn. Sem. POMI, 322 (2005),  186–211  mathnet  mathscinet  zmath; J. Math. Sci. (N. Y.), 137:2 (2006), 4722–4738  scopus 15
2003
49. A. V. Ustinov, “A Discrete Analog of the Poisson Summation Formula”, Mat. Zametki, 73:1 (2003),  106–112  mathnet  mathscinet  zmath; Math. Notes, 73:1 (2003), 97–102  isi 6
2002
50. A. V. Ustinov, “On a Diophantine inequality”, Chebyshevskii Sb., 3:1 (2002),  103–119  mathnet  mathscinet  zmath
51. A. V. Ustinov, “On some cubic equations”, Fundam. Prikl. Mat., 8:1 (2002),  263–271  mathnet  mathscinet  zmath
52. A. V. Ustinov, “A Discrete Analog of Euler's Summation Formula”, Mat. Zametki, 71:6 (2002),  931–936  mathnet  mathscinet  zmath; Math. Notes, 71:6 (2002), 851–856  isi  scopus 9
2001
53. A. V. Ustinov, “On summation and interpolation formulas”, Chebyshevskii Sb., 1:1 (2001),  52–71  mathnet  mathscinet  zmath 4
1998
54. A. V. Ustinov, “On the number of summands in the asymptotic formula for the number of solutions to Waring's equation”, Mat. Zametki, 64:2 (1998),  285–296  mathnet  mathscinet  zmath; Math. Notes, 64:2 (1998), 240–250  isi 2
2024
55. N. Panyunin, A. Ustinov, “Когда фигурные числа совпадают”, Kvant, 2024, no. 1,  32–33  mathnet
2023
56. A. Ustinov, “Последовательности Сомоса (окончание)”, Kvant, 2023, no. 9,  11–19  mathnet
57. A. Ustinov, “Последовательности Сомоса”, Kvant, 2023, no. 8,  8–14  mathnet
58. A. Ustinov, “Волшебные пятерки”, Kvant, 2023, no. 7,  41  mathnet
2010
59. A. Ustinov, “Цепные дроби вокруг нас”, Kvant, 2010, no. 2,  32–33  mathnet
2008
60. V. Vavilov, A. Ustinov, “Две знаменитые формулы”, Kvant, 2008, no. 2,  11–15  mathnet
2007
61. V. Vavilov, A. Ustinov, “Полуправильные многоугольники на решетках”, Kvant, 2007, no. 6,  13–15  mathnet
62. V. V. Vavilov, A. V. Ustinov, “Problems on Lattices, ended”, Math. Ed., 2007, no. 2(42),  33–57  mathnet
2006
63. V. Vavilov, A. Ustinov, “Окружности на решетках”, Kvant, 2006, no. 6,  10–14  mathnet
64. V. V. Vavilov, A. V. Ustinov, “Problems on Lattices”, Math. Ed., 2006, no. 4(39),  47–67  mathnet

Presentations in Math-Net.Ru
1. Последовательности Сомоса. Семинар 4
A. V. Ustinov
Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023
July 27, 2023 15:30   
2. Последовательности Сомоса. Семинар 3
A. V. Ustinov
Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023
July 25, 2023 15:30   
3. Последовательности Сомоса. Семинар 2
A. V. Ustinov
Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023
July 23, 2023 17:15   
4. Последовательности Сомоса. Семинар 1
A. V. Ustinov
Summer School “Contemporary Mathematics” Named After Vitaly Arnold, 2023
July 20, 2023 15:30   
5. Тропические последовательности Сомоса
A. V. Ustinov

November 7, 2022 16:35   
6. Скрытые теоремы сложения
A. V. Ustinov
Mathematical seminar Faculty of Computer Science HSE
October 14, 2022 18:10   
7. Шашки Фейнмана
A. V. Ustinov
Colloquium of the Faculty of Computer Science
June 7, 2022 16:20   
8. Feynman Checkers: Number Theory in Quantum Electrodynamics
A. V. Ustinov, M. B. Skopenkov
Memorial Conference on Analytic Number Theory and Applications Dedicated to the 130th Anniversary of I. M. Vinogradov
September 14, 2021 10:30   
9. Feynman Checkers: Number theory methods in quantum theory
A. V. Ustinov, M. B. Skopenkov
International conference on Analytic Number Theory dedicated to 75th anniversary of G. I. Arkhipov and S. M. Voronin
December 15, 2020 11:00   
10. Шашки Фейнмана: элементарное введение в квантовую теорию поля, занятие 4
M. B. Skopenkov, A. V. Ustinov

July 28, 2019 17:15   
11. Фризы и цепные дроби, занятие 4
A. V. Ustinov

July 28, 2019 11:15   
12. Шашки Фейнмана: элементарное введение в квантовую теорию поля, занятие 3
M. B. Skopenkov, A. V. Ustinov

July 27, 2019 11:15   
13. Шашки Фейнмана: элементарное введение в квантовую теорию поля, занятие 2
M. B. Skopenkov, A. V. Ustinov

July 26, 2019 17:15   
14. Шашки Фейнмана: элементарное введение в квантовую теорию поля, занятие 1
M. B. Skopenkov, A. V. Ustinov

July 25, 2019 09:30   
15. The Korobov polynomials
A. V. Ustinov
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 29, 2018 09:00
16. An elementary approach to Somos-$4$ sequences
Alexey V. Ustinov
International conference "Algebraic Topology, Combinatorics, and Mathematical Physics" on occasion of Victor Buchstaber's 75th birthday
May 28, 2018 15:50   
17. Зачем нужны статистики Гаусса–Кузьмина?
A. V. Ustinov
Meetings of the Moscow Mathematical Society
May 22, 2012 18:30
18. The solution of Arnold's problem on Gauss–Kuz'min statistics for finite continued fractions. Lecture 4
A. V. Ustinov
Summer School "Contemporary Mathematics", 2011
July 22, 2011 17:00   
19. The solution of Arnold's problem on Gauss–Kuz'min statistics for finite continued fractions. Lecture 3
A. V. Ustinov
Summer School "Contemporary Mathematics", 2011
July 21, 2011 09:30   
20. The solution of Arnold's problem on Gauss–Kuz'min statistics for finite continued fractions. Lecture 2
A. V. Ustinov
Summer School "Contemporary Mathematics", 2011
July 20, 2011 11:15   
21. The solution of Arnold's problem on Gauss–Kuz'min statistics for finite continued fractions. Lecture 1
A. V. Ustinov
Summer School "Contemporary Mathematics", 2011
July 19, 2011 15:30   
22. Discrete Fourier transform. I
A. V. Ustinov
Summer School "Contemporary Mathematics", 2010
July 19, 2010 11:15   
23. О статистических свойствах алгоритма Евклида и конечных цепных дробей
A. V. Ustinov
Seminar by Department of Discrete Mathematic, Steklov Mathematical Institute of RAS
February 26, 2008 16:00

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