Limiting behaviour and modular completions of MacMahon-like q-series
Number Theory
2024-07-15 v2 Combinatorics
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.
Keywords
Cite
@article{arxiv.2402.08340,
title = {Limiting behaviour and modular completions of MacMahon-like q-series},
author = {Kathrin Bringmann and William Craig and Jan-Willem van Ittersum and Badri Vishal Pandey},
journal= {arXiv preprint arXiv:2402.08340},
year = {2024}
}
Comments
22 pages; several new results were added