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Ustinov Alexey Vladimirovich

Statistics Math-Net.Ru
Total publications: 42
Scientific articles: 40
Presentations: 9

Number of views:
This page:5887
Abstract pages:14162
Full texts:2841
References:1512
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. Ustinov A. V., Applications of Kloosterman Sums in Arithmetic and Geometry, LAMBERT Academic Publishing, 2011
  2. Alfutova N. B., Ustinov A. V., Algebra and Number Theory. Collected Problems for Mathematical Schools, MCCME, Moscow, 2009
  3. Ustinov A. V., Vavilov V. V., Polygons on the lattices, MCCME, Moscow, 2006
  4. Alfutova N. B., Egorov Yu.A., Ustinov A. V., 18x18, MCCME, 2006
  5. Ustinov A. V., Vavilov V. V., Problems on the squared paper, Kolmogorov's School, 2006

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https://mathscinet.ams.org/mathscinet/MRAuthorID/647186
http://elibrary.ru/author_items.asp?authorid=115028
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Publications in Math-Net.Ru
1. The Distribution of the Rational Points on the Unit Circle
M. A. Korolev, A. V. Ustinov
Dokl. Akad. Nauk, 481:2 (2018),  0
2. Buchstaber Formal Group and Elliptic Functions of Small Levels
A. V. Ustinov
Mat. Zametki, 102:1 (2017),  96–108
3. Mechanical characteristics of molecular dynamics model and Korobov polynomials
M. A. Guzev, A. V. Ustinov
Dal'nevost. Mat. Zh., 16:1 (2016),  39–43
4. Coefficient rings of Tate formal groups determining Krichever genera
E. Yu. Bunkova, V. M. Buchstaber, A. V. Ustinov
Tr. Mat. Inst. Steklova, 292 (2016),  43–68
5. Distribution of algebraic points in domains of small measure and near the surfaces
V. I. Bernik, A. G. Gusakova, A. V. Ustinov
Chebyshevskii Sb., 16:3 (2015),  78–94
6. On Points of the Modular Hyperbola under the Graph of a Linear Function
A. V. Ustinov
Mat. Zametki, 97:2 (2015),  296–301
7. On a Generalization of Kloosterman Sums
A. V. Ustinov
Mat. Zametki, 97:1 (2015),  154–157
8. Three-dimensional continued fractions and Kloosterman sums
A. V. Ustinov
Uspekhi Mat. Nauk, 70:3(423) (2015),  107–180
9. Coefficient rings of formal group laws
V. M. Buchstaber, A. V. Ustinov
Mat. Sb., 206:11 (2015),  19–60
10. The distribution of solutions of a determinantal equation
A. V. Ustinov
Mat. Sb., 206:7 (2015),  103–134
11. On the distribution of points on the modular hyperbola
V. I. Bernik, A. V. Ustinov
Dal'nevost. Mat. Zh., 14:2 (2014),  141–155
12. On continued fractions of equal length
A. V. Ustinov
Dal'nevost. Mat. Zh., 14:1 (2014),  96–99
13. Calculation of a Gauss sum via the discrete Fourier transform
A. V. Ustinov
Dal'nevost. Mat. Zh., 14:1 (2014),  90–95
14. Сквозь сеть сопротивлений
M. B. Skopenkov, A. A. Pakharev, A. V. Ustinov
Mat. Pros., Ser. 3, 18 (2014),  33–65
15. On the Three-Dimensional Vahlen Theorem
A. V. Ustinov
Mat. Zametki, 95:1 (2014),  154–156
16. Spin chains and Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals
A. V. Ustinov
Mat. Sb., 204:5 (2013),  143–160
17. Случайные блуждания и электрические цепи
M. Skopenkov, V. Smykalov, A. V. Ustinov
Mat. Pros., Ser. 3, 16 (2012),  25–47
18. Minimal Vector Systems in 3-Dimensional Lattices and Analog of Vahlen's Theorem for 3-Dimensional Minkowski's Continued Fractions
A. V. Ustinov
Sovrem. Probl. Mat., 16 (2012),  103–128
19. Geometric proof of Rødseth's formula for Frobenius numbers
A. V. Ustinov
Tr. Mat. Inst. Steklova, 276 (2012),  280–287
20. On Voronoi's cylindric minima theorem
A. V. Ustinov
Dal'nevost. Mat. Zh., 11:2 (2011),  213–221
21. On Gauss — Kuz'min statistics in short intervals
A. V. Ustinov
Dal'nevost. Mat. Zh., 11:1 (2011),  93–98
22. Сопротивление между узлами решетки
D. Baranov, M. Skopenkov, A. Ustinov
Mat. Pros., Ser. 3, 15 (2011),  229–230
23. On the distribution of Frobenius numbers with three arguments
A. V. Ustinov
Izv. RAN. Ser. Mat., 74:5 (2010),  145–170
24. The Mean Number of Steps in the Euclidean Algorithm with Odd Incomplete Quotients
A. V. Ustinov
Mat. Zametki, 88:4 (2010),  594–604
25. On the statistical properties of elements of continued fractions
A. V. Ustinov
Dokl. Akad. Nauk, 424:4 (2009),  459–461
26. On the distribution of integer points
A. V. Ustinov
Dal'nevost. Mat. Zh., 9:1-2 (2009),  176–181
27. The statistics of particle trajectories in the inhomogeneous Sinai problem for a two-dimensional lattice
V. A. Bykovskii, A. V. Ustinov
Izv. RAN. Ser. Mat., 73:4 (2009),  17–36
28. The Mean Number of Steps in the Euclidean Algorithm with Least Absolute-Value Remainders
A. V. Ustinov
Mat. Zametki, 85:1 (2009),  153–156
29. The solution of Arnold's problem on the weak asymptotics of Frobenius numbers with three arguments
A. V. Ustinov
Mat. Sb., 200:4 (2009),  131–160
30. On the number of solutions of the congruence $xy\equiv l$ $(\operatorname{mod}q)$ under the graph of a twice continuously differentiable function
A. V. Ustinov
Algebra i Analiz, 20:5 (2008),  186–216
31. The Statistics of Particle Trajectories in the Homogeneous Sinai Problem for a Two-Dimensional Lattice
V. A. Bykovskii, A. V. Ustinov
Funktsional. Anal. i Prilozhen., 42:3 (2008),  10–22
32. Asymptotic behaviour of the first and second moments for the number of steps in the Euclidean algorithm
A. V. Ustinov
Izv. RAN. Ser. Mat., 72:5 (2008),  189–224
33. Calculation of the variance in a problem in the theory of continued fractions
A. V. Ustinov
Mat. Sb., 198:6 (2007),  139–158
34. A Short Proof of Euler's Identity for Continuants
A. V. Ustinov
Mat. Zametki, 79:1 (2006),  155–156
35. On Gauss–Kuz'min statistics for finite continued fractions
A. V. Ustinov
Fundam. Prikl. Mat., 11:6 (2005),  195–208
36. On the statistical properties of finite continued fractions
A. V. Ustinov
Zap. Nauchn. Sem. POMI, 322 (2005),  186–211
37. A Discrete Analog of the Poisson Summation Formula
A. V. Ustinov
Mat. Zametki, 73:1 (2003),  106–112
38. On a Diophantine inequality
A. V. Ustinov
Chebyshevskii Sb., 3:1 (2002),  103–119
39. On some cubic equations
A. V. Ustinov
Fundam. Prikl. Mat., 8:1 (2002),  263–271
40. A Discrete Analog of Euler's Summation Formula
A. V. Ustinov
Mat. Zametki, 71:6 (2002),  931–936
41. On summation and interpolation formulas
A. V. Ustinov
Chebyshevskii Sb., 1:1 (2001),  52–71
42. On the number of summands in the asymptotic formula for the number of solutions to Waring's equation
A. V. Ustinov
Mat. Zametki, 64:2 (1998),  285–296

43. Problems on Lattices, ended
V. V. Vavilov, A. V. Ustinov
Math. Ed., 2007, no. 2(42),  33–57
44. Problems on Lattices
V. V. Vavilov, A. V. Ustinov
Math. Ed., 2006, no. 4(39),  47–67

Presentations in Math-Net.Ru
1. 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
2. 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   
3. Зачем нужны статистики Гаусса–Кузьмина?
A. V. Ustinov
Meetings of the Moscow Mathematical Society
May 22, 2012 18:30
4. 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   
5. 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   
6. 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   
7. 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   
8. Discrete Fourier transform. I
A. V. Ustinov
Summer School "Contemporary Mathematics", 2010
July 19, 2010 11:15   
9. О статистических свойствах алгоритма Евклида и конечных цепных дробей
A. V. Ustinov
Seminar of the Department of Discrete Mathematics, Steklov Mathematical Institute of RAS
February 26, 2008 16:00

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