Traces of Hecke operators in level 1 and Gaussian hypergeometric functions
Number Theory
2011-09-16 v1
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.
Keywords
Cite
@article{arxiv.1109.3362,
title = {Traces of Hecke operators in level 1 and Gaussian hypergeometric functions},
author = {Jenny G. Fuselier},
journal= {arXiv preprint arXiv:1109.3362},
year = {2011}
}
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11 pages