Zeta functions of certain K3 families : application of the formula of Clausen

Abstract

Based on the theory of rigid cohomology, we provide an explicit formula of zeta functions of certain K3 families, which we call the hypergeometric type. The central point of our argument is the comparison between the 2nd rigid cohomology of a K3 and the symmetric product of an elliptic curve, that is brought from the classical formula of Clausen.