Arak’s Inequalities for the Generalized Arithmetic Progressions


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Abstract

In 1980s, Arak has obtained powerful inequalities for the concentration functions of sums of independent random variables. Using these results, he has solved an old problem stated by Kolmogorov. In this paper, one of Arak’s results is modified to include generalized arithmetic progressions in the statement.

About the authors

A. Yu. Zaitsev

St. Petersburg Department of the Steklov Mathematical Institute, St. Petersburg State University

Author for correspondence.
Email: zaitsev@pdmi.ras.ru
Russian Federation, St. Petersburg

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