几乎素数的更高默顿常量 II

IF 0.5 3区数学 Q3 MATHEMATICS International Journal of Number Theory Pub Date : 2024-03-20 DOI:10.1142/s179304212450088x

Jonathan Bayless, Paul Kinlaw, Jared Duker Lichtman

引用次数: 0

摘要

对于 k≥1，让ℛk(x)表示具有 k 个质因数的数到 x 的倒数和，以倍数计数。在之前的工作中，作者扩展了梅尔腾斯第二定理，得到了ℛk(x)的估计值，并对任意 N>0 的ℛ2(x)进行了更精细的估计，误差可达 (logx)-N。在本文中，我们从ℛ2(x) 估计中建立了较高默顿常量的极限行为。我们还将这些结果扩展到ℛ3(x)，并对 k≥4 的一般情况进行了评论。

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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Higher Mertens constants for almost primes II

For $k \geq 1$ , let $ℛ_{k} (x)$ denote the reciprocal sum up to $x$ of numbers with $k$ prime factors, counted with multiplicity. In prior work, the authors obtained estimates for $ℛ_{k} (x)$ , extending Mertens’ second theorem, as well as a finer-scale estimate for $ℛ_{2} (x)$ up to ${(log x)}^{- N}$ error for any $N > 0$ . In this paper, we establish the limiting behavior of the higher Mertens constants from the $ℛ_{2} (x)$ estimate. We also extend these results to $ℛ_{3} (x)$ , and we comment on the general case $k \geq 4$ .

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来源期刊

International Journal of Number Theory 数学-数学

CiteScore

1.10

自引率

14.30%

发文量

审稿时长

4-8 weeks

期刊介绍： This journal publishes original research papers and review articles on all areas of Number Theory, including elementary number theory, analytic number theory, algebraic number theory, arithmetic algebraic geometry, geometry of numbers, diophantine equations, diophantine approximation, transcendental number theory, probabilistic number theory, modular forms, multiplicative number theory, additive number theory, partitions, and computational number theory.

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