几个素数的哥德巴赫表示

IF 0.7 3区数学 Q3 MATHEMATICS

Journal of Number Theory Pub Date : 2025-08-22 DOI:10.1016/j.jnt.2025.07.008

Thi Thu Nguyen

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引用次数: 0

摘要

我们研究了整数作为k个素数和的哥德巴赫表示的平均阶数的渐近公式。我们将已有的k=2的结果推广到一般的k，并对所有大于3的k得到了更好的误差项。此外，在这种情况下，我们证明了黎曼假设与良好平均阶之间的等价性。

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Goldbach representations with several primes

We study an asymptotic formula for average orders of Goldbach representations of an integer as the sum of k primes. We extend the existing result for

k = 2

to a general k and obtain a better error term for all k larger than 3. Moreover, we prove an equivalence between the Riemann Hypothesis and a good average order in this case.

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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.