Scientific Calendar Event

Starts 9 Sep 2015 14:30
Ends 9 Sep 2015 15:30
Central European Time
Leonardo Building - Luigi Stasi Seminar Room
Abstract: Classical modular forms are holomorphic functions that are meromorphic at the cusps and satisfy nice modular symmetries. Harmonic Maass forms are real-analytic generalizations thereof in that instead of being holomorphic they are annihilated by the weight k Laplace operator. These functions generalize Maass waveforms, which are of weight 0 and decay in the cusps. Recently there has been an active interest in harmonic Maass forms, as their holomorphic parts (so-called mock modular forms) naturally occur in various areas of mathematics and physics. The probably most famous example of mock modular forms are given by Ramanujan's mock theta function which he introduced in his last letter to Hardy shortly before he died. In this talk I instead consider Maass forms which are also allowed to have poles in the upper half plane and give various applications of such functions including Hardy-Ramanujan type formulas for meromorphic modular forms. All this is joint work with Ben Kane.