Critical zeros of Dirichlet $L$-functions

TL;DR

This paper employs advanced analytic techniques to establish lower bounds on the proportion of simple zeros on the critical line for twisted Dirichlet L-functions of degrees 1, 2, or 3.

Contribution

It introduces new bounds for simple zeros of Dirichlet L-functions using the Asymptotic Large Sieve and Levinson's method, extending previous results.

Findings

Lower bounds for simple zeros on the critical line

Proportion of zeros depends on the degree of the L-function

Application of advanced sieve and Levinson's method

Abstract

We use the Asymptotic Large Sieve and Levinson's method to obtain lower bounds for the proportion of simple zeros on the critical line of the twists by primitive Dirichlet characters of a fixed L-function of degree 1,2, or 3.