Asymptotic properties of Dedekind zeta functions in families of number fields

TL;DR

This paper investigates the asymptotic behavior of Dedekind zeta functions in families of number fields under the Generalized Riemann Hypothesis, extending the Brauer--Siegel theorem and deriving new limit formulas for Euler--Kronecker constants.

Contribution

It provides a new formula describing the limit behavior of Dedekind zeta functions for Re s > 1/2 assuming GRH, generalizing existing theorems.

Findings

Derived a limit formula for Dedekind zeta functions in number field families

Extended the Brauer--Siegel theorem to broader contexts

Obtained a limit formula for Euler--Kronecker constants

Abstract

The main goal of this paper is to prove a formula that expresses the limit behaviour of Dedekind zeta functions for $\Re s > 1/2$ in families of number fields, assuming that the Generalized Riemann Hypothesis holds. This result can be viewed as a generalization of the Brauer--Siegel theorem. As an application we obtain a limit formula for Euler--Kronecker constants in families of number fields.