4 papers
Overpartitions and class numbers of binary quadratic forms
Kathrin Bringmann, Jeremy Lovejoy
We show that the Zagier-Eisenstein series shares its non-holomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank diff…
Overpartition pairs and two classes of basic hypergeometric series
Jeremy Lovejoy, Olivier Mallet
We study the combinatorics of two classes of basic hypergeometric series. We first show that these series are the generating functions for certain overpartition pairs defined by fr…
Dyson's Rank, overpartitions, and weak Maass forms
Kathrin Bringmann, Jeremy Lovejoy
In a series of papers the first author and Ono connected the rank, a partition statistic introduced by Dyson, to weak Maass forms, a new class of functions which are related to mod…
Partitions weighted by the parity of the crank
Dohoon Choi, Soon-Yi Kang, Jeremy Lovejoy
A partition statistic ` crank' gives combinatorial interpretations for Ramanujan's famous partition congruences. In this paper, we establish an asymptotic formula, Ramanujan type c…