Harmonic weak Maass forms and periods

Abstract:   In this talk we review results on several types of harmonic weak Maass forms that are related to newforms of even integer weight.  

Starting with an integral weight newform, we briefly present different constructions of integral weight harmonic weak Maass forms via (generalized) Weierstrass zeta functions that map to the newform under a certain differential operator. (Joint work with Jens Funke, Michael Mertens, Eugenia Rosu.)

A second construction via theta liftings gives a half-integral weight harmonic weak Maass form whose coefficients are given by periods of certain meromorphic modular forms with algebraic coefficients and periods of the integer even weight newform. (Joint work with Jan Bruinier and Markus Schwagenscheidt.)