Zagier-type dualities and lifting maps for harmonic Maass-Jacobi forms |
| |
Authors: | Kathrin Bringmann Olav K. Richter |
| |
Affiliation: | a Mathematisches Institut, Universität Köln, Weyertal 86-90, D-50931 Köln, Germany b Department of Mathematics, University of North Texas, Denton, TX 76203, USA |
| |
Abstract: | The real-analytic Jacobi forms of Zwegers' PhD thesis play an important role in the study of mock theta functions and related topics, but have not been part of a rigorous theory yet. In this paper, we introduce harmonic Maass-Jacobi forms, which include the classical Jacobi forms as well as Zwegers' functions as examples. Maass-Jacobi-Poincaré series also provide prime examples. We compute their Fourier expansions, which yield Zagier-type dualities and also yield a lift to skew-holomorphic Jacobi-Poincaré series. Finally, we link harmonic Maass-Jacobi forms to different kinds of automorphic forms via a commutative diagram. |
| |
Keywords: | primary, 11F50 secondary, 11F30, 11F37 |
本文献已被 ScienceDirect 等数据库收录! |
|