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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Mock modular forms as $ p$-adic modular forms


Authors: Kathrin Bringmann, Pavel Guerzhoy and Ben Kane
Journal: Trans. Amer. Math. Soc. 364 (2012), 2393-2410
MSC (2010): Primary 11F33, 11F37, 11F11
Published electronically: January 6, 2012
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Abstract: In this paper, we consider the question of correcting mock modular forms in order to obtain $ p$-adic modular forms. In certain cases we show that a mock modular form $ M^+$ is a $ p$-adic modular form. Furthermore, we prove that otherwise the unique correction of $ M^+$ is intimately related to the shadow of $ M^+$.


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Additional Information

Kathrin Bringmann
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: kbringma@math.uni-koeln.de

Pavel Guerzhoy
Affiliation: Department of Mathematics, University of Hawaii, Honolulu, Hawaii 96822-2273
Email: pavel@math.hawaii.edu

Ben Kane
Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
Email: bkane@math.uni-koeln.de

DOI: http://dx.doi.org/10.1090/S0002-9947-2012-05525-5
PII: S 0002-9947(2012)05525-5
Keywords: $p$-adic modular forms, mock theta functions, mock modular forms, harmonic weak Maass forms
Received by editor(s): March 23, 2010
Published electronically: January 6, 2012
Additional Notes: The research of the first author was supported by the Alfried Krupp Prize for Young University Teachers of the Krupp Foundation and also by NSF grant DMS-0757907. The final details of the paper were completed at the AIM workshop “Mock modular forms in combinatorics and arithmetic geometry”. The authors would like to thank AIM for their support and for supplying a stimulating work environment.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.