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math.NT2025
Ramanujan's partition generating functions modulo
Kathrin Bringmann, William Craig, Ken Ono
For the partition function , Ramanujan proved the striking identities $$ P_5(q):=\sum_{n\geq 0} p(5n+4)q^n =5\prod_{n\geq 1} \frac{\left(q^5;q^5\right)_{\infty}^5}{(q;q)_{\in…
math.NT2025
Precision Asymptotics for Partitions Featuring False-Indefinite Theta Functions
Kathrin Bringmann, William Craig, Caner Nazaroglu
Andrews-Dyson-Hickerson, Cohen build a striking relation between q-hypergeometric series, real quadratic fields, and Maass forms. Thanks to the works of Lewis-Zagier and Zwegers we…
math.NT2024
Limiting behaviour and modular completions of MacMahon-like q-series
Kathrin Bringmann, William Craig, Jan-Willem van Ittersum +1
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 prop…