Moments and One level density of certain unitary families of Hecke $L$-functions

Gao, Peng; Zhao, Liangyi

Journal de théorie des nombres de Bordeaux, Tome 33 (2021) no. 1, pp. 1-16.

Dans cet article, nous étudions les moments des valeurs centrales de certaines familles unitaires de fonctions $L$ de Hecke sur le corps des rationnels de Gauss et prouvons un résultat quantitatif de non-annulation de leurs valeurs centrales. Nous établissons aussi un résultat de densité portant sur les petits zéros dans ces familles de fonctions $L$ de Hecke.

In this paper, we study the moments of central values of certain unitary families of Hecke $L$-functions of the Gaussian field, and establish quantitative non-vanishing result for their central values. We also establish a one level density result for the low-lying zeros of these families of Hecke $L$-functions.

Classification : 11M41, 11L40
Mots clés : Hecke $L$-functions, Hecke characters

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