title: Lifting cusp forms to Maass forms with an application to partitions.
abstract: For 2 < k [abstract: see text] we define lifts of cuspidal Poincaré series in S(k)(Gamma(0)(N)) to weight 2 - k harmonic weak Maass forms. This construction answers a question of Dyson by providing the general framework "explaining" Ramanujan's mock theta functions. As an application, we show that the number of partitions of a positive integer n is the "trace" of singular moduli of a Maass form arising from the lift of a weight 4 cusp form corresponding to a Calabi-Yau threefold.
authors.affiliation: Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA.
authors.forename: Kathrin
authors.initials: K
authors.lastname: Bringmann
authors.forename: Ken
authors.initials: K
authors.lastname: Ono