Sur l'annulation de la valeur centrale de la fonction L de Hecke

TL;DR

This paper proves that for certain weights, there exist cuspidal eigenforms whose Hecke L-functions do not vanish at the central point, extending previous results in modular form theory.

Contribution

It demonstrates the existence of cuspidal eigenforms with non-vanishing Hecke L-functions at the central point for all weights divisible by 4 and greater than 12.

Findings

Existence of non-vanishing Hecke L-functions at the central point for specified weights

Extension of previous non-vanishing results to a broader class of weights

Supports conjectures on the distribution of zeros of L-functions

Abstract

In this note, following results from Henri Cohen and Winfried Kohnen, we show that for all integer k greater than 12 and divisible by 4, there exists a cuspidal eigenform of weight k for the full modular group SL2(Z) such that its Hecke L-function does not vanish on k/2.