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

TL;DR

This paper derives explicit formulas for the zeta functions of specific K3 surface families of hypergeometric type using rigid cohomology and Clausen's classical formula, linking K3 cohomology to elliptic curves.

Contribution

It introduces a new explicit formula for zeta functions of hypergeometric type K3 families based on rigid cohomology and classical Clausen formulas.

Findings

Explicit zeta function formulas for certain K3 families.

Connection established between K3 cohomology and elliptic curves.

Application of classical Clausen formula in modern cohomological context.

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.