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Hecke operators for weakly holomorphic modular forms and supersingular congruences

Author: P. Guerzhoy
Journal: Proc. Amer. Math. Soc. 136 (2008), 3051-3059
MSC (2000): Primary 11F37, 11F33
Published electronically: April 29, 2008
MathSciNet review: 2407067
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Abstract: We consider the action of Hecke operators on weakly holomorphic modular forms and a Hecke-equivariant duality between the spaces of holomorphic and weakly holomorphic cusp forms. As an application, we obtain congruences modulo supersingular primes, which connect Hecke eigenvalues and certain singular moduli.

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Additional Information

P. Guerzhoy
Affiliation: Department of Mathematics, University of Hawaii at Manoa, 2565 McCarthy Mall, Honolulu, Hawaii 96822-2273

Received by editor(s): April 23, 2007
Received by editor(s) in revised form: July 16, 2007
Published electronically: April 29, 2008
Additional Notes: This work is supported by NSF grant DMS-0700933
Communicated by: Ken Ono
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.