Large values of logarithmic derivatives of quadratic Dirichlet $L$-functions

TL;DR

This paper uses the resonance method to establish conditional Omega results for the logarithmic derivatives of quadratic Dirichlet L-functions, improving and generalizing previous findings in the field.

Contribution

It introduces new conditional Omega results for these derivatives, enhancing previous bounds and extending earlier theorems by Mortada, Murty, and Yang.

Findings

Improved Omega bounds for logarithmic derivatives

Generalized results of Yang on L-functions

Extended previous work by Mortada and Murty

Abstract

In this article, we apply the resonance method to derive conditional Omega results for logarithmic derivatives of quadratic Dirichlet $L$-functions. We improve a previous result of Mortada and Murty \cite{MM13}, as well as generalize some results of Yang \cite{yang2023omegatheoremslogarithmicderivatives}.