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

Akio Nakagawa

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arXiv · 2111.15054

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

Akio Nakagawa

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Abstract

We compute the Artin $L$-function of a diagonal hypersurface D_{\lambda} over a finite field associated to a character of a finite group acting on D_{\lambda} , 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.

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Akio Nakagawa. 2021-11-30. Artin $L$-functions of diagonal hypersurfaces and generalized hypergeometric functions over finite fields. https://arxiv.org/abs/2111.15054

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