Simple zeros of modular L-functions

TL;DR

Under the assumption of the generalized Riemann hypothesis, this paper provides quantitative estimates for counting simple zeros on the critical line of L-functions associated with classical holomorphic newforms.

Contribution

It offers new quantitative bounds for simple zeros of modular L-functions on the critical line, assuming the generalized Riemann hypothesis.

Findings

Quantitative estimates for simple zeros on the critical line.

Conditional results based on the generalized Riemann hypothesis.

Abstract

Assuming the generalized Riemann hypothesis, we prove quantitative estimates for the number of simple zeros on the critical line for the L-functions attached to classical holomorphic newforms.