English

$p$-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 pp-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 pp-adic hypergeometric functions. One conjecture of Evans behaves as a bridge to connect pp-adic hypergeometric functions with Kloosterman sheaf sum. We also connect pp-adic hypergeometric functions with Fourier coefficients of certain modular forms.

Keywords

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}
}
R2 v1 2026-06-23T13:10:54.963Z