MacMahonesque配分函数检测与素数相关的集合

IF 0.5 4区数学 Q3 MATHEMATICS

Archiv der Mathematik Pub Date : 2025-04-02 DOI:10.1007/s00013-025-02109-x

Kevin Gomez

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引用次数: 0

摘要

Craig， van Ittersum和Ono最近的工作在MacMahon的配分函数中构造了检测素数的显式表达式。进一步，他们定义了广义的MacMahonesque函数，并证明了在这些函数中有无限多个这样的表达式。在这里，我们展示了如何修改和调整它们的结构来检测质数的立方以及等差数列中的质数。

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MacMahonesque partition functions detect sets related to primes

Recent work by Craig, van Ittersum, and Ono constructs explicit expressions in the partition functions of MacMahon that detect the prime numbers. Furthermore, they define generalizations, the MacMahonesque functions, and prove there are infinitely many such expressions in these functions. Here, we show how to modify and adapt their construction to detect cubes of primes as well as primes in arithmetic progressions.

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来源期刊

Archiv der Mathematik 数学-数学

CiteScore

1.10

自引率

0.00%

发文量

117

审稿时长

4-8 weeks

期刊介绍： Archiv der Mathematik (AdM) publishes short high quality research papers in every area of mathematics which are not overly technical in nature and addressed to a broad readership.