Universität zu Köln

Roehrig, Christina and Zwegers, Sander (2022). Theta series for quadratic forms of signature (n-1, 1) with (spherical) polynomials. Int. J. Number Theory, 18 (7). S. 1491 - 1516. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. ISSN 1793-7310

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Abstract

We construct almost. holomorphic and holomorphic modular forms by considering theta series for quadratic forms of signature (n - 1, 1). We include homogeneous and spherical polynomials in the definition of the theta series (generalizing a construction of the second author) to obtain holomorphic, almost holomorphic and modular theta series. We give a criterion for these series to coincide, enabling us to construct almost holomorphic and holomorphic cusp forms on congruence subgroups of the modular group. Further, we provide numerous explicit examples.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Roehrig, Christina UNSPECIFIED UNSPECIFIED UNSPECIFIED Zwegers, Sander UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-660320
DOI:	10.1142/S1793042122500762
Journal or Publication Title:	Int. J. Number Theory
Volume:	18
Number:	7
Page Range:	S. 1491 - 1516
Date:	2022
Publisher:	WORLD SCIENTIFIC PUBL CO PTE LTD
Place of Publication:	SINGAPORE
ISSN:	1793-7310
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language MODULAR-FORMS Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/66032