Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms
Journal article, 2016

We investigate Poincare series, where we average products of terms of Fourier series of real-analytic Siegel modular forms. There are some (trivial) special cases for which the products of terms of Fourier series of elliptic modular forms and harmonic Maass forms are almost holomorphic, in which case the corresponding Poincare series are almost holomorphic as well. In general, this is not the case. The main point of this paper is the study of Siegel-Poincare series of degree 2 attached to products of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms. We establish conditions on the convergence and nonvanishing of such Siegel-Poincare series. We surprisingly discover that these Poincare series are almost holomorphic Siegel modular forms, although the product of terms of Fourier series of harmonic Siegel-Maass forms and holomorphic Siegel modular forms (in contrast to the elliptic case) is not almost holomorphic. Our proof employs tools from representation theory. In particular, we determine some constituents of the tensor product of Harish-Chandra modules with walls.

modular-forms

representations

conjecture

degenerate principal series

Author

Kathrin Bringmann

Olav K. Richter

Martin Raum

Chalmers, Mathematical Sciences, Algebra and geometry

University of Gothenburg

RESEARCH IN THE MATHEMATICAL SCIENCES

2197-9847 (ISSN)

Vol. 3 Art. no. 30-

Subject Categories

Mathematics

DOI

10.1186/s40687-016-0080-y

More information

Created

12/28/2017