Limiting behaviour and modular completions of MacMahon-like q-series

2024/02/13 by Kathrin Bringmann, William Craig, Bringmann, Kathrin +5
Mathematics · #11A25 #11F03 #11F11 #11F50 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Mathematical Identities #Combinatorics (math.CO) #FOS: Mathematics #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2402.08340

openalex publication_date 2024/02/13 · openalex created_date 2024/02/15 · openalex updated_date 2026/07/30

Abstract

Recently, MacMahon's generalized sum-of-divisor functions were shown to link partitions, quasimodular forms, and q-multiple zeta values. In this paper, we explore many further properties and extensions of these. Firstly, we address a question of Ono by producing infinite families of MacMahon-like functions that approximate the colored partition functions (and indeed other eta quotients). We further explore the MacMahon-like functions and discover new and suggestive arithmetic structure and modular completions.

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