Kohnen's limit process for real-analytic Siegel modular forms
Number Theory
2012-06-12 v3
Abstract
Kohnen introduced a limit process for Siegel modular forms that produces Jacobi forms. He asked if there is a space of real-analytic Siegel modular forms such that skew-holomorphic Jacobi forms arise via this limit process. In this paper, we initiate the study of harmonic skew-Maass-Jacobi forms and harmonic Siegel-Maass forms. We improve a result of Maass on the Fourier coefficients of harmonic Siegel-Maass forms, which allows us to establish a connection to harmonic skew-Maass-Jacobi forms. In particular, we answer Kohnen's question in the affirmative.
Cite
@article{arxiv.1105.5482,
title = {Kohnen's limit process for real-analytic Siegel modular forms},
author = {Kathrin Bringmann and Martin Raum and Olav Richter},
journal= {arXiv preprint arXiv:1105.5482},
year = {2012}
}
Comments
19 pages, accepted for publication in Advances in Mathematics