Dwork hypersurfaces of degree six and Greene's hypergeometric function

DOI10.32917/H2020097arXiv2010.13079MaRDI QIDQ6352176

Publication date: 25 October 2020

Abstract: In this paper, we give a formula for the number of rational points on the Dwork hypersurfaces of degree six over finite fields by using Greene's finite-field hypergeometric function, which is a generalization of Goodson's formula for the Dwork hypersurfaces of degree four. Our formula is also a higher-dimensional and a finite field analogue of Matsumoto-Terasoma-Yamazaki's formula. Furthermore, we also explain the relation between our formula and Miyatani's formula.

Mathematics Subject Classification ID

Rational points (14G05) Finite ground fields in algebraic geometry (14G15) Other character sums and Gauss sums (11T24) Generalized hypergeometric series, ({}_pF_q) (33C20) Varieties over finite and local fields (11G25)

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