An extension of smooth numbers: Multiple dense divisibility

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-09-23 DOI:10.1016/j.jnt.2025.08.013

Garo Sarajian , Andreas Weingartner

引用次数: 0

Abstract

The i-tuply y-densely divisible numbers were introduced by a Polymath project, as a weaker condition on the moduli than y-smoothness, in distribution estimates for primes in arithmetic progressions. We obtain the order of magnitude of the count of these integers up to x, uniformly in x and y, for every fixed natural number i.

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光滑数的推广：多重稠密可整除性

一个Polymath项目引入了i-tuply y-密可整除数，作为等差数列中素数分布估计中模的一个弱条件。对于每一个固定的自然数i，我们得到这些整数的数量级，直到x，在x和y上一致。

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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来源期刊

Journal of Number Theory 数学-数学

CiteScore

1.30

自引率

14.30%

发文量

122

审稿时长

16 weeks

期刊介绍： The Journal of Number Theory (JNT) features selected research articles that represent the broad spectrum of interest in contemporary number theory and allied areas. A valuable resource for mathematicians, the journal provides an international forum for the publication of original research in this field. The Journal of Number Theory is encouraging submissions of quality, long articles where most or all of the technical details are included. The journal now considers and welcomes also papers in Computational Number Theory. Starting in May 2019, JNT will have a new format with 3 sections: JNT Prime targets (possibly very long with complete proofs) high impact papers. Articles published in this section will be granted 1 year promotional open access. JNT General Section is for shorter papers. We particularly encourage submission from junior researchers. Every attempt will be made to expedite the review process for such submissions. Computational JNT . This section aims to provide a forum to disseminate contributions which make significant use of computer calculations to derive novel number theoretic results. There will be an online repository where supplementary codes and data can be stored.