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q-series and weight 3/2 Maass forms

Part of: Basic hypergeometric functions Discontinuous groups and automorphic forms

Published online by Cambridge University Press:  01 May 2009

Kathrin Bringmann ,
Amanda Folsom  and
Ken Ono
Kathrin Bringmann
Affiliation:
Mathematisches Institut, Universität Köln, Weyertal 86-90, D-50931 Köln, Germany (email: kbringma@math.uni-koeln.de)
Amanda Folsom
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA (email: folsom@math.wisc.edu)
Ken Ono
Affiliation:
Department of Mathematics, University of Wisconsin, Madison, WI 53706, USA (email: ono@math.wisc.edu)
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Abstract

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Despite the presence of many famous examples, the precise interplay between basic hypergeometric series and modular forms remains a mystery. We consider this problem for canonical spaces of weight 3/2 harmonic Maass forms. Using recent work of Zwegers, we exhibit forms that have the property that their holomorphic parts arise from Lerch-type series, which in turn may be formulated in terms of the Rogers–Fine basic hypergeometric series.

Keywords

Mock theta functionsharmonic Maass forms

MSC classification

Secondary: 11F37: Forms of half-integer weight; nonholomorphic modular forms 33D15: Basic hypergeometric functions in one variable, $_rphi_s$
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 3 , May 2009 , pp. 541 - 552
Copyright
Copyright © Foundation Compositio Mathematica 2009

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