Universität zu Köln

Schwagenscheidt, Markus ORCID: 0000-0002-8214-3106 (2019). Borcherds lifts of harmonic Maass forms and modular integrals. Math. Ann., 375 (3-4). S. 1615 - 1648. HEIDELBERG: SPRINGER HEIDELBERG. ISSN 1432-1807

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Abstract

We extend Borcherds' singular theta lift in signature (1,2) to harmonic Maass forms of weight 1/2 whose non-holomorphic part is allowed to be of exponential growth at i infinity. We determine the singularities of the lift and compute its Fourier expansion. It turns out that the lift is continuous but not differentiable along certain geodesics in the upper half-plane corresponding to the non-holomorphic principal part of the input. As an application, we obtain a generalization to higher level of the weight 2 modular integral of Duke, Imamoglu and Toth. Further, we construct automorphic products associated to harmonic Maass forms.

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:38-126729
DOI:	10.1007/s00208-019-01903-7
Journal or Publication Title:	Math. Ann.
Volume:	375
Number:	3-4
Page Range:	S. 1615 - 1648
Date:	2019
Publisher:	SPRINGER HEIDELBERG
Place of Publication:	HEIDELBERG
ISSN:	1432-1807
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language AUTOMORPHIC-FORMS Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/12672