On the Zeta Function of a Family of Quintics

Philippe Goutet (1)

1 IMJ - Institut de Mathématiques de Jussieu

In this article, we give a proof of the link between the zeta function of two families of hypergeometric curves and the zeta function of a family of quintics that was observed numerically by Candelas, de la Ossa, and Rodriguez Villegas. The method we use is based on formulas of Koblitz and various Gauss sums identities; it does not give any geometric information on the link.

Mots clés: quintic threefold; hypergeometric curves; zeta function factorization; dwork hypersurface

Domaines: Théorie des nombres [math.NT]

Philippe Goutet. On the Zeta Function of a Family of Quintics. 2007. ⟨hal-00405347⟩