Non vanishing of Central values of modular L-functions for Hecke eigenforms of level one

TL;DR

This paper investigates the nonvanishing of central values of twisted modular L-functions associated with level one Hecke eigenforms, contributing to understanding their behavior at the critical point.

Contribution

It provides new results on the nonvanishing of central L-values for level one Hecke eigenforms, advancing knowledge in the analytic properties of modular L-functions.

Findings

Proves nonvanishing results for twisted L-functions at the central point.

Establishes conditions under which the central values do not vanish.

Enhances understanding of the distribution of non-zero central L-values.

Abstract

Let F(z) be a newform of weight 2k and level one with a trivial character, and assume that F(z) is a non-zero eigenform of all Hecke operators. In this paper, we study nonvanishing for central values of twisted modular L-function of F.