On adelic Hurwitz zeta measures

TL;DR

This paper constructs a measure on the profinite integers that unifies p-adic Hurwitz zeta functions across all primes, advancing the understanding of p-adic zeta functions in number theory.

Contribution

It introduces a novel $\hat ext{ extbf{Z}}$-valued measure that interpolates p-adic Hurwitz zeta functions for all primes simultaneously.

Findings

Unified p-adic Hurwitz zeta measure constructed

Interpolates all p-adic Hurwitz zeta functions

Provides new tools for p-adic number theory

Abstract

In this paper we construct a $\hat\mathbb{Z}$-valued measure on $\hat\mathbb{Z}$ which interpolates $p$-adic Hurwitz zeta functions for all $p$.