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arXiv · 1109.3362

Traces of Hecke operators in level 1 and Gaussian hypergeometric functions

Jenny G. Fuselier
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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 2F1-hypergeometric functions, extending previous work of the author to all odd primes p, instead of only those p=1 (mod 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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Jenny G. Fuselier. 2011-09-15. Traces of Hecke operators in level 1 and Gaussian hypergeometric functions. https://arxiv.org/abs/1109.3362

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