On the frequency of vanishing of quadratic twists of modular L-functions

TL;DR

This paper explores the frequency of zeros in quadratic twists of modular L-functions using a combination of theoretical insights and numerical experiments inspired by random matrix theory.

Contribution

It introduces a new approach linking random matrix theory to the conjecture on vanishings of quadratic twists of modular L-functions, supported by both theory and numerical evidence.

Findings

Evidence supports the random matrix model predictions

Numerical data aligns with conjectured vanishings frequency

Theoretical framework connects L-functions with matrix ensembles

Abstract

We present theoretical and numerical evidence for a random matrix theoretic approach to a conjecture about vanishings of quadratic twists of certain L-functions