Explicit Deuring-Heilbronn phenomenon for Dirichlet $L$-functions

TL;DR

This paper proves an explicit zero repulsion phenomenon for Dirichlet L-functions assuming a Landau-Siegel zero, providing uniform estimates across the critical strip and improving previous bounds.

Contribution

It introduces a new explicit estimate for the Deuring-Heilbronn phenomenon that is uniform in the critical strip and improves upon prior results.

Findings

Established explicit zero repulsion under Landau-Siegel zero assumption.

Provided uniform estimates across the entire critical strip.

Improved previous explicit bounds by Thorner and Zaman.

Abstract

Assuming the existence of a Landau-Siegel zero, we establish an explicit Deuring-Heilbronn zero repulsion phenomenon for Dirichlet $L$-functions modulo $q$. Our estimate is uniform in the entire critical strip, and improves over the previous best known explicit estimate due to Thorner and Zaman.