Mock modular forms as $p$-adic modular forms
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- by Kathrin Bringmann, Pavel Guerzhoy and Ben Kane PDF
- Trans. Amer. Math. Soc. 364 (2012), 2393-2410 Request permission
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 $M^+$.References
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Additional Information
- Kathrin Bringmann
- Affiliation: Mathematical Institute, University of Cologne, Weyertal 86-90, 50931 Cologne, Germany
- MR Author ID: 774752
- 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
- MR Author ID: 789505
- Email: bkane@math.uni-koeln.de
- 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 âMock modular forms in combinatorics and arithmetic geometryâ. The authors would like to thank AIM for their support and for supplying a stimulating work environment.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 364 (2012), 2393-2410
- MSC (2010): Primary 11F33, 11F37, 11F11
- DOI: https://doi.org/10.1090/S0002-9947-2012-05525-5
- MathSciNet review: 2888211