## Traces of Hecke operators in level 1 and Gaussian hypergeometric functions

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**141**(2013), 1871-1881 Request permission

## Abstract:

We provide formulas for traces of $p^{th}$ Hecke operators in level 1 in terms of values of finite field $_2F_1$-hypergeometric functions, extending previous work of the author to all odd primes $p$ instead of only those $p \equiv 1 \pmod {12}$. We first give a general level 1 trace formula in terms of the trace of Frobenius on a family of elliptic curves, and then we draw on recent work of Lennon to produce level 1 trace formulas in terms of hypergeometric functions for all primes $p > 3$.## References

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## Additional Information

**Jenny G. Fuselier**- Affiliation: Department of Mathematics and Computer Science, High Point University, High Point, North Carolina 27262
- MR Author ID: 882190
- Email: jfuselie@highpoint.edu
- Received by editor(s): September 15, 2011
- Published electronically: December 10, 2012
- Communicated by: Ken Ono
- © Copyright 2012
American Mathematical Society

The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc.
**141**(2013), 1871-1881 - MSC (2010): Primary 11F30; Secondary 11T24, 11G20, 33C99
- DOI: https://doi.org/10.1090/S0002-9939-2012-11540-0
- MathSciNet review: 3034414