Coefficients of Harmonic maass forms

Abstract

Harmonic Maass forms have recently been related to many different topics in number theory: Ramanujan's mock theta functions, Dyson's rank generating functions, Borcherds products, and central values and derivatives of quadratic twists of modular L-functions. Motivated by these connections, we obtain exact formulas for the coefficients of harmonic Maass forms of nonpositive weight, and we obtain a conditional result for such forms of weight 1/2. This extends earlier work of Rademacher and Zuckerman in the case of weakly holomorphic modular forms of negative weight. © Springer Science+Business Media, LLC 2012.