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Ustinov, Alexey Vladimirovich

Statistics Math-Net.Ru
Total publications: 48
Scientific articles: 46
Presentations: 14

Number of views:
This page:7403
Abstract pages:19133
Full texts:5279
References:1934
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)
Phone: +7 (4212) 32 46 76
Fax: +7 (4212) 32 46 76
E-mail:
Website: http://iam.khv.ru/staff/Ustinov.php
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. 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
  2. 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
  3. A. V. Ustinov, “The solution of Arnolds problem on the weak asymptotics of Frobenius numbers with three arguments”, Mat. Sb., 200:4 (2009), 131–160  mathnet  crossref  mathscinet  zmath  adsnasa  elib; Sb. Math., 200:4 (2009), 597–627  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
2019
1. A. V. Ustinov, “A simplified proof of Ward's formula for elliptic sequences”, Dal'nevost. Mat. Zh., 19:1 (2019),  84–87  mathnet
2. 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  elib
3. 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; Izv. Math., 83:5 (2019), 1008–1049  isi
4. A. V. Ustinov, “On Formal Buchstaber Groups of Special Form”, Mat. Zametki, 105:6 (2019),  899–910  mathnet  elib; Math. Notes, 105:6 (2019), 894–904  isi  scopus
5. I. S. Vorob'ev, A. V. Ustinov, “Symmetric semigroups with three generators”, Mat. Sb., 210:12 (2019),  31–42  mathnet; Sb. Math., 210:12 (2019), 1690–1701  isi  scopus
6. A. V. Ustinov, “An Elementary Approach to the Study of Somos Sequences”, Tr. Mat. Inst. Steklova, 305 (2019),  330–343  mathnet  elib; Proc. Steklov Inst. Math., 305 (2019), 305–317  isi  scopus
2018
7. 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
8. 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
2016
9. 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
10. E. Yu. Bunkova, V. M. Buchstaber, A. V. Ustinov, “Coefficient rings of Tate formal groups determining Krichever genera”, Tr. Mat. Inst. Steklova, 292 (2016),  43–68  mathnet  mathscinet  zmath  elib; Proc. Steklov Inst. Math., 292 (2016), 37–62  isi  elib  scopus
2015
11. 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
12. 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
13. 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
14. 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
15. 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
16. 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
2014
17. 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
18. A. V. Ustinov, “On continued fractions of equal length”, Dal'nevost. Mat. Zh., 14:1 (2014),  96–99  mathnet
19. A. V. Ustinov, “Calculation of a Gauss sum via the discrete Fourier transform”, Dal'nevost. Mat. Zh., 14:1 (2014),  90–95  mathnet
20. M. B. Skopenkov, A. A. Pakharev, A. V. Ustinov, “Сквозь сеть сопротивлений”, Mat. Pros., Ser. 3, 18 (2014),  33–65  mathnet
21. 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
2013
22. 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
2012
23. M. Skopenkov, V. Smykalov, A. V. Ustinov, “Случайные блуждания и электрические цепи”, Mat. Pros., Ser. 3, 16 (2012),  25–47  mathnet
24. 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
25. A. V. Ustinov, “Geometric proof of Rødseth's formula for Frobenius numbers”, Tr. Mat. Inst. Steklova, 276 (2012),  280–287  mathnet  mathscinet  elib; Proc. Steklov Inst. Math., 276 (2012), 275–282  isi  elib  scopus
2011
26. A. V. Ustinov, “On Voronoi's cylindric minima theorem”, Dal'nevost. Mat. Zh., 11:2 (2011),  213–221  mathnet
27. A. V. Ustinov, “On Gauss — Kuz'min statistics in short intervals”, Dal'nevost. Mat. Zh., 11:1 (2011),  93–98  mathnet
28. D. Baranov, M. Skopenkov, A. Ustinov, “Сопротивление между узлами решетки”, Mat. Pros., Ser. 3, 15 (2011),  229–230  mathnet
2010
29. 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
30. 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
2009
31. 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
32. A. V. Ustinov, “On the distribution of integer points”, Dal'nevost. Mat. Zh., 9:1-2 (2009),  176–181  mathnet  elib
33. 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
34. 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
35. 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
2008
36. 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
37. 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
38. 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
2007
39. 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
2006
40. 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
2005
41. 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
42. 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
2003
43. 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
2002
44. A. V. Ustinov, “On a Diophantine inequality”, Chebyshevskii Sb., 3:1 (2002),  103–119  mathnet  mathscinet  zmath
45. A. V. Ustinov, “On some cubic equations”, Fundam. Prikl. Mat., 8:1 (2002),  263–271  mathnet  mathscinet  zmath
46. 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
2001
47. A. V. Ustinov, “On summation and interpolation formulas”, Chebyshevskii Sb., 1:1 (2001),  52–71  mathnet  mathscinet  zmath
1998
48. 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

2007
49. V. V. Vavilov, A. V. Ustinov, “Problems on Lattices, ended”, Math. Ed., 2007, 2(42),  33–57  mathnet
2006
50. V. V. Vavilov, A. V. Ustinov, “Problems on Lattices”, Math. Ed., 2006, 4(39),  47–67  mathnet

Presentations in Math-Net.Ru
1. Шашки Фейнмана: элементарное введение в квантовую теорию поля, занятие 4
M. B. Skopenkov, A. V. Ustinov

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

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

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

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

July 25, 2019 09:30   
6. 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
7. 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   
8. Зачем нужны статистики Гаусса–Кузьмина?
A. V. Ustinov
Meetings of the Moscow Mathematical Society
May 22, 2012 18:30
9. 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   
10. 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   
11. 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   
12. 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   
13. Discrete Fourier transform. I
A. V. Ustinov
Summer School "Contemporary Mathematics", 2010
July 19, 2010 11:15   
14. 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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