Universität zu Köln

Olivetto, Rene (2014). On the Fourier coefficients of meromorphic Jacobi forms. Int. J. Number Theory, 10 (6). S. 1519 - 1541. SINGAPORE: WORLD SCIENTIFIC PUBL CO PTE LTD. ISSN 1793-7310

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Abstract

In this paper, we describe the automorphic properties of the Fourier coefficients of meromorphic Jacobi forms. Extending results of Dabholkar, Murthy, and Zagier, and Bringmann and Folsom, we prove that the canonical Fourier coefficients of a meromorphic Jacobi form phi (z; tau) are the holomorphic parts of some (vector- valued) almost harmonic Maass forms. We also give a precise description of their completions, which turn out to be uniquely determined by the Laurent coefficients of phi at each pole, as well as some well-known real analytic functions, that appear for instance in the completion of Appell-Lerch sums.

Item Type:	Journal Article
Creators:	Creators Email ORCID ORCID Put Code Olivetto, Rene UNSPECIFIED UNSPECIFIED UNSPECIFIED
URN:	urn:nbn:de:hbz:38-430614
DOI:	10.1142/S1793042114500419
Journal or Publication Title:	Int. J. Number Theory
Volume:	10
Number:	6
Page Range:	S. 1519 - 1541
Date:	2014
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 Mathematics Multiple languages
URI:	http://kups.ub.uni-koeln.de/id/eprint/43061