所有乘法函数的频谱，以及对强力数的应用

IF 0.6 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2024-03-21 DOI:10.1016/j.jnt.2024.02.011

Tsz Ho Chan

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引用次数: 0

摘要

粗略地说，乘法函数谱是所有可能均值的集合。在本文中，我们对支持幂级数的乘法函数谱感兴趣。我们证明其实数对数谱的取值范围为-2/(4+2)=-0.26160...至1，而已知所有自然数上实数乘法函数的对数谱的取值范围为 0 至 1。在这一研究过程中，我们修正并完成了格兰维尔和桑达拉拉詹关于所有乘法函数谱的证明。

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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Spectrum of all multiplicative functions with application to powerfull numbers

Roughly speaking, the spectrum of multiplicative functions is the set of all possible mean values. In this paper, we are interested in the spectra of multiplicative functions supported over powerfull numbers. We prove that its real logarithmic spectrum takes values from $- \sqrt{2} / (4 + \sqrt{2}) = - 0.26160 . . .$ to 1 while it is known that the logarithmic spectrum of real multiplicative functions over all natural numbers takes values from 0 to 1. In the course of this study, we correct and complete the proof of Granville and Soundararajan on the spectrum of all multiplicative functions.

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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.