Hypergeometric Decompositions of K3 Surface Pencils

Abstract: In this talk we will look at five pencils of projective quartic surfaces with the aim of giving explicit formulas for the point counts over finite fields of each. These point counts are written in terms of hypergeometric sums. Given time, we will discuss how to obtain a decomposition of the incomplete L-function of each pencil in terms of hypergeometric L-series and Dedekind zeta functions. This is joint work with Rachel Davis, Jessamyn Dukes, Thais Gomes Ribeiro, Eli Orvis, Adriana Salerno, and Ursula Whitcher.

number theory

Audience: researchers in the topic

Five College Number Theory Seminar