On the value-distributions of logarithmic derivatives of Dedekind zeta functions

TL;DR

This paper investigates the value distributions of the logarithmic derivatives of Dedekind zeta functions across algebraic number fields, constructing their density functions via Fourier transforms of infinite product representations.

Contribution

It introduces a method to explicitly determine the density functions of these value distributions for any algebraic number field.

Findings

Density functions characterized as Fourier inverse transforms.

Explicit formulas derived from Euler product representations.

Applicable to all algebraic number fields.

Abstract

We study the distributions of values of the logarithmic derivatives of the Dedekind zeta functions on a fixed vertical line. The main object is determining and investigating the density functions of such value-distributions for any algebraic number field. We construct the density functions as the Fourier inverse transformations of certain functions represented by infinite products that come from the Euler products of the Dedekind zeta functions.