m函数和螺旋函数：在哥德巴赫问题和黎曼ζ函数零点中的应用

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-10-02 DOI:10.1016/j.jnt.2025.09.013

Kohji Matsumoto , Masatoshi Suzuki

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引用次数: 0

摘要

研究了描述哥德巴赫计数函数求和函数渐近公式中次主项值分布的极限定理的m函数。其中一个新的方面是由m函数的一些公式提供的黎曼假设的充分条件，这是以前工作中的必要条件。另一个新的方面是次要主项与螺旋函数之间的关系，这为黎曼假设提供了另一个充分必要条件。我们通过公理化的方法研究了广义环境下的m函数和螺旋函数。

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M-functions and screw functions: Applications to Goldbach's problem and zeros of the Riemann zeta-function

We study the M-functions, which describe the limit theorem for the value-distributions of the secondary main terms in the asymptotic formulas for the summatory functions of the Goldbach counting function. One of the new aspects is a sufficient condition for the Riemann hypothesis provided by some formulas of the M-functions, which was a necessary condition in previous work. The other new aspect is the relation between the secondary main terms and the screw functions, which provides another necessary and sufficient condition for the Riemann hypothesis. We study such M-functions and screw functions in generalized settings by axiomatizing them.

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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.