On Selberg’s Central Limit Theorem for Dirichlet L-functions
Po-Han Hsu ; Peng-Jie Wong
Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 685-710.

Dans cet article, nous présentons une nouvelle preuve du théorème central limite de Selberg pour les fonctions L de Dirichlet, basée sur une méthode de Radziwiłł et Soundararajan. De plus, nous étudions la propriété d’indépendance pour les variables aléatoires apparaissant dans ce théoréme central limite.

In this article, based on a method of Radziwiłł and Soundararajan, we present a new proof of Selberg’s central limit theorem for Dirichlet L-functions. Also, we study the independence property for the random variables arising from such a central limit theorem.

Reçu le : 2019-05-06
Révisé le : 2020-03-03
Accepté le : 2020-10-24
Publié le : 2021-01-08
DOI : https://doi.org/10.5802/jtnb.1139
Classification : 11M06
Mots clés : Dirichlet L-functions, value distribution, central limit theorem, independence 
@article{JTNB_2020__32_3_685_0,
     author = {Po-Han Hsu and Peng-Jie Wong},
     title = {On Selberg's Central Limit Theorem for Dirichlet $L$-functions},
     journal = {Journal de Th\'eorie des Nombres de Bordeaux},
     pages = {685--710},
     publisher = {Soci\'et\'e Arithm\'etique de Bordeaux},
     volume = {32},
     number = {3},
     year = {2020},
     doi = {10.5802/jtnb.1139},
     language = {en},
     url = {https://jtnb.centre-mersenne.org/item/JTNB_2020__32_3_685_0/}
}
Po-Han Hsu; Peng-Jie Wong. On Selberg’s Central Limit Theorem for Dirichlet $L$-functions. Journal de Théorie des Nombres de Bordeaux, Tome 32 (2020) no. 3, pp. 685-710. doi : 10.5802/jtnb.1139. https://jtnb.centre-mersenne.org/item/JTNB_2020__32_3_685_0/

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