Universität zu Köln

Ehlen, Stephan ORCID: 0000-0003-2029-6219 (2017). CM VALUES OF REGULARIZED THETA LIFTS AND HARMONIC WEAK MAASS FORMS OF WEIGHT 1. Duke Math. J., 166 (13). S. 2447 - 2520. DURHAM: DUKE UNIV PRESS. ISSN 1547-7398

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Abstract

We study special values of regularized theta lifts at complex multiplication (CM) points. In particular; we show that CM values of Borcherds products can be expressed in terms of finitely many Fourier coefficients of certain harmonic weak Maafi forms of weight 1. As it turns out, these coefficients are logarithms of algebraic integers whose prime ideal factorization is determined by special cycles on an arithmetic curve. Our results imply a conjecture of Duke and Li and give a new proof of the modularity of a certain arithmetic generating series of weight 1 studied by Kudla, Rapoport, and Yang.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Ehlen, Stephan UNSPECIFIED orcid.org/0000-0003-2029-6219 UNSPECIFIED
URN:	urn:nbn:de:hbz:38-217648
DOI:	10.1215/00127094-2017-0005
Journal or Publication Title:	Duke Math. J.
Volume:	166
Number:	13
Page Range:	S. 2447 - 2520
Date:	2017
Publisher:	DUKE UNIV PRESS
Place of Publication:	DURHAM
ISSN:	1547-7398
Language:	English
Faculty:	Faculty of Mathematics and Natural Sciences
Divisions:	Faculty of Mathematics and Natural Sciences > Department of Mathematics and Computer Science > Mathematical Institute
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language EISENSTEIN SERIES; DERIVATIVES; CYCLES Multiple languages Mathematics Multiple languages
Refereed:	Yes
URI:	http://kups.ub.uni-koeln.de/id/eprint/21764