Arak’s Inequalities for the Generalized Arithmetic Progressions


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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.

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A. Zaitsev

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

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Email: zaitsev@pdmi.ras.ru
俄罗斯联邦, St. Petersburg

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