MacMahonesque partition functions detect sets related to primes

2024/09/21 by Kevin Gómez, Gomez, Kevin · 2 citations
Computer Science · Mathematics · #05A17 (Primary) 11Fxx (Secondary) #11P81 #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #FOS: Mathematics #Graph Labeling and Dimension Problems #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2409.14253

openalex publication_date 2024/09/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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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• Prime detecting quasi-modular forms in higher level
• Quasimodular forms that detect primes are Eisenstein

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