4 papers
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…
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…
On the asymptotic behavior for partitions separated by parity
Kathrin Bringmann, William Craig, Caner Nazaroglu
The study of partitions with parts separated by parity was initiated by Andrews in connection with Ramanujan's mock theta functions, and his variations on this theme have produced…
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…