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Трехмерные аналоги тождеств Хис-Брауна и Сельберга
Доклады Российской Академии Наук. Математика, Информатика, Процессы управления. Россия. 2020. Т. 494. № 1. С. 14–16.
Ustinov A., Быковский В. А.
Language:
Russian
Ustinov A., LAP LAMBERT Academic Publishing, 2011.
The book is devoted to applications of Kloosterman sum estimates in various problems of number theory. ...
Added: October 13, 2025
Быковский В. А., Ustinov A., Функциональный анализ и его приложения 2008 Т. 42 № 3 С. 10–22
In this paper, we generalize and refine some results by F. P. Boca, R. N. Gologan, and A. Zaharescu on the asymptotic behavior as h→0 of the statistics of the free path length until the first hit of the h-neighborhood (a disk of radius h) of a nonzero integer for a particle issuing from the origin. The established facts imply that the limit distribution ...
Added: October 11, 2025
Ustinov A., Алгебра и анализ 2008 Т. 20 № 5 С. 186–216
A result by V. A.Bykovskiĭ (1981) on the number of solutions of the congruence xy≡l (modq) under the graph of a twice continuously differentiable function is refined. As an application, Porter's result (1975) on the mean number of steps in the Euclid algorithm is sharpened and extended to the case of Gauss–Kuzmin statistics. ...
Added: October 11, 2025
Ustinov A., Математический сборник 2009 Т. 200 № 4 С. 131–160
It is shown that on the average the Frobenius numbers f(a,b,c) behave like 8/π√abc . ...
Added: October 11, 2025
Ustinov A., Быковский В. А., Известия РАН. Серия математическая 2009 Т. 73 № 4 С. 17–36
In connection with the two-dimensional model known as the ‘periodic Lorentz gas’, we study the asymptotic behaviour of statistical characteristics of a free path interval of a point particle before its first occurrence in an h-neighbourhood (a circle of radius h) of a non-zero integer point as h→0 given that the particle starts from the h-neighbourhood of the origin. We evaluate the limit distribution ...
Added: October 10, 2025
Ustinov A., Дальневосточный математический журнал 2009 Т. 9 № 1-2 С. 176–181
We study distribution of distances from primitive integer points to the origin. ...
Added: October 10, 2025
Ustinov A., Известия РАН. Серия математическая 2010 Т. 74 № 5 С. 145–170
We prove the existence of the limit density distribution for normalized Frobenius numbers with three arguments. The density is found explicitly. ...
Added: October 9, 2025
Ustinov A., Дальневосточный математический журнал 2011 Т. 11 № 1 С. 93–98
The article is devoted to investigation of Gauss — Kuz'min statistics for rational numbers a/b, where b is fixed, 1⩽a⩽b, (a,b)=1. New asymptotic formula for the mean value of Gauss — Kuz'min statistics is proved. It sharpens previous result which is similar to the Porter's theorem. ...
Added: October 9, 2025
Ustinov A., Математический сборник 2013 Т. 204 № 5 С. 143–160
New results related to number theoretic model of spin chains are proved. We solve Arnold's problem on the Gauss-Kuz'min statistics for quadratic irrationals. ...
Added: October 9, 2025
Ustinov A., Берник В. И., Дальневосточный математический журнал 2014 Т. 14 № 2 С. 141–155
It is known that solutions of determinant equation det∣∣axyz∣∣=q are uniformly distributed. The article contains similar results when the variables satisfy additional restrictions (a,x)=1 or (a,x,y,z)=1. ...
Added: October 9, 2025
Ustinov A., Математический сборник 2015 Т. 206 № 7 С. 103–134
In 1964, Linnik and Skubenko established the equidistribution of the integral points on the determinantal surface detX=P, where X is a (3×3) matrix with independent entries and P is an increasing parameter. Their method involved reducing the problem by one dimension (that is, to the determinantal equations with a (2×2) matrix). In this paper a more precise version of the Linnik-Skubenko reduction is proposed. It ...
Added: October 9, 2025
Ustinov A., Успехи математических наук 2015 Т. 70 № 3 С. 107–180
This survey is devoted to results related to metric properties of classical continued fractions and Voronoi–Minkowski three-dimensional continued fractions. The main focus is on applications of analytic methods based on estimates of Kloosterman sums. An apparatus is developed for solving problems about three-dimensional lattices. The approach is based on reduction to the preceding dimension, an ...
Added: October 9, 2025
Khrabrov A. I., В кн.: Задачи Санкт-Петербургской олимпиады школьников по математике 2018 года.: М.: МЦНМО, 2019. С. 130–159.
Число e и простые числа ...
Added: June 28, 2019
Maslov V., Теоретическая и математическая физика 2018 Т. 196 № 1 С. 161–166
Since the deep paper by Bohr and Kalckar in 1938, it has been known that the Ramanujan formula in
number theory is related to statistical physics and nuclear theory. From the early 1970s, there have been
attempts to generalize number theory from the space of integers to the space of rational numbers, i.e., to
construct a so-called analytic ...
Added: October 30, 2018
Kalmynin A. B., Современные проблемы математики 2017 № 24 С. 7–45
Статья содержит обзор докладов международной Конференции памяти А.А. Карацубы по теории чисел и приложениям, прошедшей с 28 по 30 января 2016 года в Математическом институте им. В.А. Стеклова и на механико-математическом факультете МГУ. ...
Added: November 23, 2017
Chernyshev V. L., Minenkov D. S., Nazaikinskii V. E., / Series math "arxiv.org". 2016. No. 1604.03509.
For any k>1, we find the asymptotics of the counting function of k-th power-free elements in an additive arithmetic semigroup with exponential growth of the abstract prime counting function. This paper continues the authors' earlier research dealing with the case of infinite k. ...
Added: April 13, 2016
Gritsenko V., Hulek K., Sankaran G., Compositio Mathematica 2010 Vol. 146 No. 2 P. 404–434
We study the moduli spaces of polarised irreducible symplectic manifolds. By a comparison with locally symmetric varieties of orthogonal type of dimension 20, we show that the moduli space of 2d polarised (split type) symplectic manifolds which are deformation equivalent to degree 2 Hilbert schemes of a K3 surface is of general type if d ...
Added: March 3, 2015
Lazarev A. A., Kvaratskhelia A., Доклады Академии наук 2010 Т. 432 № 6 С. 746–749
Одним из актуальных вопросов разработки математической теории расписаний является построение метрик, которые можно использовать при разработке точных и приближенных алгоритмов решения задач. Введение метрических пространств для $NP$-трудных задач теории расписаний позволяет применять общие математические подходы к нахождению приближенного решения с гарантированной абсолютной погрешностью. Ранее для $NP$-трудных задач с критерием минимизации максимального временн\'ого смещения $\{P,R,Q\}|prec,r_j|\{L_{\max},C_{\max}\}$ была ...
Added: November 23, 2012