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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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A formula and a congruence for Ramanujan’s $\tau$-function
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by Matthew Papanikolas PDF
Proc. Amer. Math. Soc. 134 (2006), 333-341 Request permission


We determine formulas for Ramanujan’s $\tau$-function and for the coefficients of modular forms on $\Gamma _0(2)$ in terms of finite field ${}_3F_2$-hypergeometric functions. Using these formulas we obtain a new congruence of $\tau (p) \pmod {11}$.
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Additional Information
  • Matthew Papanikolas
  • Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
  • Email:
  • Received by editor(s): April 27, 2004
  • Received by editor(s) in revised form: September 9, 2004
  • Published electronically: June 14, 2005
  • Additional Notes: This research was supported by NSF grant DMS-0340812 and NSA grant MDA904-03-1-0019
  • Communicated by: Wen-Ching Winnie Li
  • © Copyright 2005 American Mathematical Society
    The copyright for this article reverts to public domain 28 years after publication.
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 333-341
  • MSC (2000): Primary 11F30; Secondary 11F33, 11T24, 33C99
  • DOI:
  • MathSciNet review: 2175999