关于积分部分集合中元素的最大公因数的分布

IF 0.3 Q4 MATHEMATICS

Acta et Commentationes Universitatis Tartuensis de Mathematica Pub Date : 2023-05-27 DOI:10.12697/acutm.2023.27.04

Teerapat Srichan

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引用次数: 0

摘要

当x→∞时，两个正整数n, m≤x为相对素数的概率趋于1/ζ(2) = 6/π2，这是一个经典的结果。在本文中，当n和m被限制为子序列，即Piatetski-Shapiro序列、Beatty序列和底函数集时，同样的结果仍然成立。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the distribution of the greatest common divisor of the elements in integral part sets

It is a classical result that the probability that two positive integers n, m ≤ x are relatively prime tends to 1/ζ(2) = 6/π2 as x → ∞. In this paper, the same result is still true when n and m are restricted to sub-sequences, i.e. Piatetski–Shapiro sequence, Beatty sequence and the floor function set.

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来源期刊

Acta et Commentationes Universitatis Tartuensis de Mathematica MATHEMATICS-

CiteScore

0.60

自引率

33.30%

发文量