## A formula and a congruence for Ramanujan’s $\tau$-function

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- Proc. Amer. Math. Soc.
**134**(2006), 333-341 Request permission

## Abstract:

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 $\tau (p) \pmod {11}$.## References

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## Additional Information

**Matthew Papanikolas**- Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843
- Email: map@math.tamu.edu
- 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: https://doi.org/10.1090/S0002-9939-05-08029-9
- MathSciNet review: 2175999