Linear statistics for zeros of Riemann's zeta function

Chris Hughes; Zeév Rudnick

doi:10.1016/S1631-073X(02)02541-4

Linear statistics for zeros of Riemann's zeta function
[Statisiques linéaires pour les zéros de la fonction zêta de Riemann]

Chris Hughes ¹ ; Zeév Rudnick ¹

¹ Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

Comptes Rendus. Mathématique, Volume 335 (2002) no. 8, pp. 667-670.

Résumé
Abstract

Nous considérons une fonction de comptage lisse des zéros de la fonction zêta de Riemann, normalisés au voisinage de la hauteur T. Nous montrons que les premiers moments sont Gaussiens, le nombre exact de tels moments dépendant de la moyenne choisie et de la fonction de comptage des zéros.

We consider a smooth counting function of the scaled zeros of the Riemann zeta function, around height T. We show that the first few moments tend to the Gaussian moments, with the exact number depending on the statistic considered.

Reçu le : 2002-08-29
Accepté le : 2002-09-02
Publié le : 2002-09-17

DOI : 10.1016/S1631-073X(02)02541-4

Affiliations des auteurs :

Chris Hughes ¹ ; Zeév Rudnick ¹

¹ Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel

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Chris Hughes; Zeév Rudnick. Linear statistics for zeros of Riemann's zeta function. Comptes Rendus. Mathématique, Volume 335 (2002) no. 8, pp. 667-670. doi : 10.1016/S1631-073X(02)02541-4. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02541-4/

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