Overpartitions and class numbers of binary quadratic forms.
We show that the Zagier-Eisenstein series shares its nonholomorphic part with certain weak Maass forms whose holomorphic parts are generating functions for overpartition rank differences. This has a number of consequences, including exact formulas, asymptotics, and congruences for the rank differences as well as q-series identities of the mock theta type.
Bringmann
Kathrin
K
Mathematisches Institut, Universität Köln, Weyertal 86-90, D-50931 Cologne, Germany. kbringma@math.uni-koeln.de
Lovejoy
Jeremy
J