Moments and One level density of certain unitary families of Hecke L-functions
Journal de Théorie des Nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 1-16.

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.

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.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/jtnb.1149
Classification: 11M41,  11L40
Keywords: Hecke L-functions, Hecke characters
Peng Gao 1; Liangyi Zhao 2

1 School of Mathematical Sciences Beihang University Beijing 100191, China
2 School of Mathematics and Statistics University of New South Wales Sydney NSW 2052, Australia
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Peng Gao; Liangyi Zhao. Moments and One level density of certain unitary families of Hecke $L$-functions. Journal de Théorie des Nombres de Bordeaux, Volume 33 (2021) no. 1, pp. 1-16. doi : 10.5802/jtnb.1149. https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1149/

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