Traces of Hecke operators in level 1 and Gaussian hypergeometric functions

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

2011-09-15

arxiv.org/abs/1109.3362v1

Mathematics

Number Theory

11 pages

Scientific paper

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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