On Selberg’s Central Limit Theorem for Dirichlet L-functions
Po-Han Hsu1 ; Peng-Jie Wong2
1 Department of Mathematics Louisiana State University Baton Rouge, LA, 70803, United States of America
2 Department of Mathematics and Computer Science University of Lethbridge Lethbridge, Alberta T1K 3M4, Canada
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.

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DOI : 10.5802/jtnb.1139
Classification : 11M06
Mots clés : Dirichlet $L$-functions, value distribution, central limit theorem, independence
Po-Han Hsu 1 ; Peng-Jie Wong 2

1 Department of Mathematics Louisiana State University Baton Rouge, LA, 70803, United States of America
2 Department of Mathematics and Computer Science University of Lethbridge Lethbridge, Alberta T1K 3M4, Canada
Licence : CC-BY-ND 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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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/articles/10.5802/jtnb.1139/

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