Motivic Modularity of CM K3 Surfaces

TL;DR

This paper provides an explicit description of the Hecke characters and base fields associated with the L-functions of CM K3 surfaces, building on foundational work by Piatetski-Shapiro and Shafarevich.

Contribution

It explicitly characterizes the Hecke characters and base fields involved in the L-functions of CM K3 surfaces, advancing understanding of their modularity.

Findings

Explicit descriptions of Hecke characters for CM K3 surfaces

Identification of base fields related to these L-functions

Enhanced understanding of the modularity of CM K3 surfaces

Abstract

Piatetski-Shapiro and Shafarevich proved the L-functions of K3 surfaces of CM type are expressed as the product of some Hecke L-functions by changing their base fields. In this paper, the aurhor gives the explicit description of these Hecke characters and base fields.