On l-adic Galois L-functions

TL;DR

This paper explores Galois actions on fundamental groups, constructing measures on products of Z_p to compute coefficients of Galois representations, linking to p-adic L-functions and zeta functions.

Contribution

It introduces a method to construct measures from towers of coverings to analyze Galois representations and connect to p-adic L-functions.

Findings

Constructed measures on products of Z_p from towers of coverings.

Calculated coefficients of Galois representations using these measures.

Connected measures to Kubota-Leopoldt p-adic L-functions and p-adic Hurwitz zeta functions.

Abstract

We are studing Galois actions on fundamental groups. Using towers of coverings we construct measures on the products of finite copies of Z_p. Using these measures we can calculate coefficients of Galois representations. In the simplest case of measures on Z_p, we get Kubota_Leopoldt p-adic L-functions and p-adic Hurwitz zeta functions.