Artin $L$-functions of diagonal hypersurfaces and generalized hypergeometric functions over finite fields

Abstract

We compute the Artin $L$-function of a diagonal hypersurface D_λ over a finite field associated to a character of a finite group acting on D_λ , and under some condition, express it in terms of hypergeometric functions and Jacobi sums over the finite field. As an application, we consider the Dwork hypersurfaces and obtain relations among certain hypergeometric functions over different finite fields.

21pages

References in corpus (2)

• Transformations of Well-Poised Hypergeometric Functions over Finite Fields
• Zeta functions of certain K3 families : application of the formula of Clausen

Cited by in corpus (1)

• Hypergeometric functions over finite fields