Traces of Hecke operators in level 1 and Gaussian hypergeometric functions

Fuselier, Jenny

doi:10.1090/S0002-9939-2012-11540-0

Traces of Hecke operators in level 1 and Gaussian hypergeometric functions
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by Jenny G. Fuselier

Proc. Amer. Math. Soc. 141 (2013), 1871-1881

DOI: https://doi.org/10.1090/S0002-9939-2012-11540-0

Published electronically: December 10, 2012

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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 $p > 3$.

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