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

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DOI : https://doi.org/10.5802/jtnb.1149
Classification : 11M41,  11L40
Mots clés : Hecke L-functions, Hecke characters
@article{JTNB_2021__33_1_1_0,
     author = {Peng Gao and Liangyi Zhao},
     title = {Moments and {One} level density of certain unitary families of {Hecke} $L$-functions},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {1--16},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {33},
     number = {1},
     year = {2021},
     doi = {10.5802/jtnb.1149},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/articles/10.5802/jtnb.1149/}
}
Peng Gao; Liangyi Zhao. Moments and One level density of certain unitary families of Hecke $L$-functions. Journal de Théorie des Nombres de Bordeaux, Tome 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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