### Skapa referens, olika format (klipp och klistra)

**Harvard**

Bringmann, K., Richter, O. och Westerholt-Raum, M. (2016) *Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms*.

** BibTeX **

@article{

Bringmann2016,

author={Bringmann, Kathrin and Richter, Olav K. and Westerholt-Raum, Martin},

title={Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms},

journal={RESEARCH IN THE MATHEMATICAL SCIENCES},

issn={2197-9847},

volume={3},

pages={Art. no. 30},

abstract={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.},

year={2016},

keywords={degenerate principal series, modular-forms, representations, conjecture},

}

** RefWorks **

RT Journal Article

SR Electronic

ID 254115

A1 Bringmann, Kathrin

A1 Richter, Olav K.

A1 Westerholt-Raum, Martin

T1 Almost holomorphic Poincare series corresponding to products of harmonic Siegel-Maass forms

YR 2016

JF RESEARCH IN THE MATHEMATICAL SCIENCES

SN 2197-9847

VO 3

AB 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.

LA eng

DO 10.1186/s40687-016-0080-y

LK http://dx.doi.org/10.1186/s40687-016-0080-y

OL 30