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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Hecke operators for weakly holomorphic modular forms and supersingular congruences
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by P. Guerzhoy PDF
Proc. Amer. Math. Soc. 136 (2008), 3051-3059 Request permission

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
  • Email: pavel@math.hawaii.edu
  • 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
  • © Copyright 2008 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 136 (2008), 3051-3059
  • MSC (2000): Primary 11F37, 11F33
  • DOI: https://doi.org/10.1090/S0002-9939-08-09277-0
  • MathSciNet review: 2407067