Scholarlink

<p>Introduced in 1920 as a generalization of the sum-of-divisors function, the MacMahon partition function has recently attracted renewed interest due to its connection with quasi-modular forms. In this article, we explicitly establish the quasi-modularity of the level <i>N</i> MacMahon function, originally studied by MacMahon himself, by employing the polynomials introduced by Lehmer in his investigation of cyclotomic polynomials. As applications, we explore analogues and extensions of the prime-detecting expressions proposed by Craig, van Ittersum, and Ono.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Quasi-modularity in MacMahon partition variants and prime detection

  • 期刊论文

  • 发表日期：

    2025年6月9日

查看全文
  • Soon-Yi Kang,
  • Toshiki Matsusaka,
  • Gyucheol Shin

摘要

Introduced in 1920 as a generalization of the sum-of-divisors function, the MacMahon partition function has recently attracted renewed interest due to its connection with quasi-modular forms. In this article, we explicitly establish the quasi-modularity of the level N MacMahon function, originally studied by MacMahon himself, by employing the polynomials introduced by Lehmer in his investigation of cyclotomic polynomials. As applications, we explore analogues and extensions of the prime-detecting expressions proposed by Craig, van Ittersum, and Ono.