Tohoku Mathematical Journal
2025
March
SECOND SERIES VOL. 77, NO. 1

Tohoku Math. J.
77 (2025), 33-53

Title ZETA FUNCTIONS OF CERTAIN K3 FAMILIES: APPLICATION OF THE FORMULA OF CLAUSEN

Author Masanori Asakura

(Received September 17, 2021, revised April 14, 2023)
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 surface and the symmetric product of the 1st rigid cohomology of an elliptic curve, that is brought from the classical formula of Clausen.

Mathematics Subject Classification. Primary 14J28; Secondary 11M38, 33C20, 14F30.
Key words and phrases. K3 surface, Zeta function, Hypergeometric function, $p$-adic cohomology.

To the top of this page

Back to the Contents