Universität zu Köln

Bringmann, Kathrin, Ehlen, Stephan and Schwagenscheidt, Markus ORCID: 0000-0002-8214-3106 (2021). On the Modular Completion of Certain Generating Functions. Int. Math. Res. Notices, 2021 (8). S. 6331 - 6373. OXFORD: OXFORD UNIV PRESS. ISSN 1687-0247

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Abstract

We complete several generating functions to non-holomorphic modular forms in two variables. For instance, we consider the generating function of a natural family of meromorphic modular forms of weight two. We then show that this generating series can be completed to a smooth, non-holomorphic modular form of weights 3/2 and two. Moreover, it turns out that the same function is also a modular completion of the generating function of weakly holomorphic modular forms of weight 3/2, which prominently appear in work of Zagier [27] on traces of singular moduli.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Bringmann, Kathrin UNSPECIFIED UNSPECIFIED UNSPECIFIED Ehlen, Stephan UNSPECIFIED UNSPECIFIED UNSPECIFIED Schwagenscheidt, Markus UNSPECIFIED orcid.org/0000-0002-8214-3106 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-566290
DOI:	10.1093/imrn/rnz338
Journal or Publication Title:	Int. Math. Res. Notices
Volume:	2021
Number:	8
Page Range:	S. 6331 - 6373
Date:	2021
Publisher:	OXFORD UNIV PRESS
Place of Publication:	OXFORD
ISSN:	1687-0247
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language CM VALUES; FORMS; TRACES Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/56629