$p$-Adic hypergeometric functions in the connections with certain twisted Kloosterman sheaf sum and modular forms
Number Theory
2020-01-15 v1
Abstract
In this paper we establish certain identities connecting -adic hypergeometric functions with 4-th twisted Kloosterman sheaf sum. To prove these identities we express certain character sum over finite field in terms of special values of -adic hypergeometric functions. One conjecture of Evans behaves as a bridge to connect -adic hypergeometric functions with Kloosterman sheaf sum. We also connect -adic hypergeometric functions with Fourier coefficients of certain modular forms.
Cite
@article{arxiv.2001.04838,
title = {$p$-Adic hypergeometric functions in the connections with certain twisted Kloosterman sheaf sum and modular forms},
author = {Neelam Saikia},
journal= {arXiv preprint arXiv:2001.04838},
year = {2020}
}