Quantitative estimates for simple zeros of L-functions

TL;DR

This paper extends a previous method to provide quantitative estimates for the distribution of simple zeros in L-functions associated with modular forms of any conductor, enhancing understanding of their zeros' behavior.

Contribution

It generalizes an existing method to handle modular form L-functions with arbitrary conductor, offering new quantitative estimates for their simple zeros.

Findings

Established bounds on simple zeros of modular form L-functions.

Extended previous methods to a broader class of L-functions.

Provided quantitative estimates applicable to arbitrary conductors.

Abstract

We generalize a method of Conrey and Ghosh (Invent. Math. 94 (1988)) to prove quantitative estimates for simple zeros of modular form L-functions of arbitrary conductor.