Universität zu Köln

Schwagenscheidt, Markus ORCID: 0000-0002-8214-3106 (2018). Eisenstein series for the Weil representation. J. Number Theory, 193. S. 74 - 91. SAN DIEGO: ACADEMIC PRESS INC ELSEVIER SCIENCE. ISSN 1096-1658

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Abstract

We compute the Fourier expansion of vector valued Eisenstein series for the Weil representation associated to an even lattice. To this end, we define certain twists by Dirichlet characters of the usual Eisenstein series associated to isotropic elements in the discriminant form of the underlying lattice. These twisted functions still form a generating system for the space of Eisenstein series but their Fourier coefficients have better multiplicative properties than the coefficients of the individual Eisenstein series. We adapt a method of Bruinier and Kuss to obtain algebraic formulas for the Fourier coefficients of the twisted Eisenstein series in terms of special values of Dirichlet L-functions and representation numbers modulo prime powers of the underlying lattice. In particular, we obtain that the Fourier coefficients of the individual Eisenstein series are rational numbers. Additionally, we show that the twisted Eisenstein series are eigenforms of the Hecke operators on vector valued modular forms introduced by Bruinier and Stein. (C) 2018 Elsevier Inc. All rights reserved.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Schwagenscheidt, Markus UNSPECIFIED orcid.org/0000-0002-8214-3106 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-164894
DOI:	10.1016/j.jnt.2018.05.014
Journal or Publication Title:	J. Number Theory
Volume:	193
Page Range:	S. 74 - 91
Date:	2018
Publisher:	ACADEMIC PRESS INC ELSEVIER SCIENCE
Place of Publication:	SAN DIEGO
ISSN:	1096-1658
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language AUTOMORPHIC PRODUCTS; FORMS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/16489