Quasi-modularity in MacMahon partition variants and prime detection
Soon-Yi Kang, Toshiki Matsusaka, Gyucheol Shin
TL;DR
This paper advances the understanding of MacMahon's partition functions by exploring their quasi-modular properties and introducing new prime-detecting expressions, building on prior foundational work.
Contribution
It offers a refined analysis of MacMahon's partition functions, revealing their quasi-modular nature and proposing novel prime detection formulas.
Findings
Identification of quasi-modular properties of partition functions
Development of new prime-detecting expressions
Extension of previous results by Craig, van Ittersum, and Ono
Abstract
Building on the results of Craig, van Ittersum, and Ono, we provide a refined understanding of MacMahon's partition functions and their variants, including their quasi-modular properties and new prime-detecting expressions.
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Taxonomy
TopicsAdvanced Mathematical Identities · Advanced Algebra and Geometry · Analytic Number Theory Research