Path Integrals and p-adic L-functions

TL;DR

This paper establishes an arithmetic path integral formula for the inverse p-adic absolute values of Kubota-Leopoldt p-adic L-functions at roots of unity, linking p-adic analysis with algebraic number theory.

Contribution

It introduces a novel path integral approach to analyze p-adic L-functions, providing new insights into their arithmetic properties.

Findings

Derived an explicit path integral formula for p-adic L-functions

Connected p-adic L-values with arithmetic path integrals

Enhanced understanding of p-adic L-functions at roots of unity

Abstract

We prove an arithmetic path integral formula for the inverse p-adic absolute values of the Kubota-Leopoldt p-adic L-functions at roots of unity.