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math.NT2007
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…
math.NT2007
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…
math.NT2007
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…