Universität zu Köln

Alfes-Neumann, Claudia and Schwagenscheidt, Markus (2021). SHINTANI THETA LIFTS OF HARMONIC MAASS FORMS. Trans. Am. Math. Soc., 374 (4). S. 2297 - 2340. PROVIDENCE: AMER MATHEMATICAL SOC. ISSN 1088-6850

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Abstract

We define a regularized Shintani theta lift which maps weight 2k + 2 (k is an element of Z, k >= 0) harmonic Maass forms for congruence subgroups to (sesqui-)harmonic Maass forms of weight 3/2 + k for the Weil representation of an even lattice of signature (1, 2). We show that its Fourier coefficients are given by traces of CM values and regularized cycle integrals of the input harmonic Maass form. Further, the Shintani theta lift is related via the xi-operator to the Millson theta lift studied in our earlier work. We use this connection to construct xi-preimages of Zagier's weight 1/2 generating series of singular moduli and of some of Ramanujan's mock theta functions.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Alfes-Neumann, Claudia UNSPECIFIED UNSPECIFIED UNSPECIFIED Schwagenscheidt, Markus UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-573782
DOI:	10.1090/tran/8265
Journal or Publication Title:	Trans. Am. Math. Soc.
Volume:	374
Number:	4
Page Range:	S. 2297 - 2340
Date:	2021
Publisher:	AMER MATHEMATICAL SOC
Place of Publication:	PROVIDENCE
ISSN:	1088-6850
Language:	English
Faculty:	Unspecified
Divisions:	Unspecified
Subjects:	no entry
Uncontrolled Keywords:	Keywords Language HALF-INTEGRAL WEIGHT; MODULAR-FORMS; HEEGNER POINTS; CM VALUES; COEFFICIENTS; DERIVATIVES; TRACES Multiple languages Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/57378