Universität zu Köln

Opitz, Sebastian and Schwagenscheidt, Markus ORCID: 0000-0002-8214-3106 (2019). HOLOMORPHIC BORCHERDS PRODUCTS OF SINGULAR WEIGHT FOR SIMPLE LATTICES OF ARBITRARY LEVEL. Proc. Amer. Math. Soc., 147 (11). S. 4639 - 4654. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6826

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Abstract

We classify the holomorphic Borcherds products of singular weight for all simple lattices of signature (2, n) with n >= 3. In addition to the automorphic products of singular weight for the simple lattices of square free level found by Dittmann, Hagemeier, and the second author, we obtain several automorphic products of singular weight 1/2 for simple lattices of signature (2, 3). We interpret them as Siegel modular forms of genus 2 and explicitly describe them in terms of the ten even theta constants. In order to rule out further holomorphic Borcherds products of singular weight, we derive estimates for the Fourier coefficients of vector valued Eisenstein series, which are of independent interest.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Opitz, Sebastian UNSPECIFIED UNSPECIFIED UNSPECIFIED Schwagenscheidt, Markus UNSPECIFIED orcid.org/0000-0002-8214-3106 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-129965
DOI:	10.1090/proc/14650
Journal or Publication Title:	Proc. Amer. Math. Soc.
Volume:	147
Number:	11
Page Range:	S. 4639 - 4654
Date:	2019
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6826
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language AUTOMORPHIC PRODUCTS; EISENSTEIN SERIES; FORMS Multiple languages Mathematics, Applied; Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/12996