Explicit zero density theorems for Dedekind zeta functions

TL;DR

This paper develops explicit formulas and bounds for the zeros of Dedekind zeta functions, enhancing understanding of their distribution with effective estimates and phenomena.

Contribution

It introduces a smooth explicit formula for Dedekind zeta zeros and derives an effective Deuring-Heilbronn phenomenon, providing explicit zero bounds.

Findings

Established a smooth explicit formula for Dedekind zeta zeros

Derived an effective version of the Deuring-Heilbronn phenomenon

Obtained explicit bounds for the number of zeros in a given region

Abstract

This article studies the zeros of Dedekind zeta functions. In particular, we establish a smooth explicit formula for these zeros and we derive an effective version of the Deuring-Heilbronn phenomenon. In addition, we obtain an explicit bound for the number of zeros in a box.