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On cycle integrals of weakly holomorphic modular forms

Published online by Cambridge University Press:  16 February 2015

KATHRIN BRINGMANN ,
PAVEL GUERZHOY  and
BEN KANE
KATHRIN BRINGMANN
Affiliation:
Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany. e-mail: kbringma@math.uni-koeln.de
PAVEL GUERZHOY
Affiliation:
Department of Mathematics, University of Hawaii, Honolulu, HI 96822-2273, U.S.A. e-mail: pavel@math.hawaii.edu
BEN KANE
Affiliation:
Department of Mathematics, University of Hong Kong, Pokfulam, Hong Kong. e-mail: bkane@maths.hku.hk
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Abstract

In this paper, we investigate cycle integrals of weakly holomorphic modular forms. We show that these integrals coincide with the cycle integrals of classical cusp forms. We use these results to define a Shintani lift from integral weight weakly holomorphic modular forms to half-integral weight holomorphic modular forms.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 158 , Issue 3 , May 2015 , pp. 439 - 449
Copyright
Copyright © Cambridge Philosophical Society 2015 

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