On logarithmic derivatives of zeta functions in families of global fields

TL;DR

This paper establishes a formula for the limit of logarithmic derivatives of zeta functions across families of global fields, extending the explicit Brauer-Siegel theorem to broader contexts with explicit error estimates.

Contribution

It generalizes the explicit Brauer-Siegel theorem by deriving a limit formula for logarithmic derivatives of zeta functions in global field families with explicit error bounds.

Findings

Derived a limit formula for logarithmic derivatives of zeta functions

Extended the explicit Brauer-Siegel theorem to new settings

Provided explicit error terms in the formula

Abstract

We prove a formula for the limit of logarithmic derivatives of zeta functions in families of global fields with an explicit error term. This can be regarded as a rather far reaching generalization of the explicit Brauer-Siegel theorem both for number fields and function fields.