Comptes Rendus
no. 8
Linear statistics for zeros of Riemann's zeta function
[Statisiques linéaires pour les zéros de la fonction zêta de Riemann]
Chris Hughes1 ; Zeév Rudnick1
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.

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 :
Accepté le :
Publié le :
DOI : 10.1016/S1631-073X(02)02541-4
Chris Hughes 1 ; Zeév Rudnick 1

1 Raymond and Beverly Sackler School of Mathematical Sciences, Tel Aviv University, Tel Aviv 69978, Israel 
@article{CRMATH_2002__335_8_667_0,
     author = {Chris Hughes and Ze\'ev Rudnick},
     title = {Linear statistics for zeros of {Riemann's} zeta function},
     journal = {Comptes Rendus. Math\'ematique},
     pages = {667--670},
     publisher = {Elsevier},
     volume = {335},
     number = {8},
     year = {2002},
     doi = {10.1016/S1631-073X(02)02541-4},
     language = {en},
}
TY  - JOUR
AU  - Chris Hughes
AU  - Zeév Rudnick
TI  - Linear statistics for zeros of Riemann's zeta function
JO  - Comptes Rendus. Mathématique
PY  - 2002
SP  - 667
EP  - 670
VL  - 335
IS  - 8
PB  - Elsevier
DO  - 10.1016/S1631-073X(02)02541-4
LA  - en
ID  - CRMATH_2002__335_8_667_0
ER  - 
%0 Journal Article
%A Chris Hughes
%A Zeév Rudnick
%T Linear statistics for zeros of Riemann's zeta function
%J Comptes Rendus. Mathématique
%D 2002
%P 667-670
%V 335
%N 8
%I Elsevier
%R 10.1016/S1631-073X(02)02541-4
%G en
%F CRMATH_2002__335_8_667_0
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/

[1] A. Fujii Explicit formulas and oscillations (D.A. Hejhal; J. Friedman; M.C. Gutzwiller; A.M. Odlyzko, eds.), Emerging Applications of Number Theory, Springer, 1999, pp. 219-267

[2] C.P. Hughes; Z. Rudnick Linear statistics of low-lying zeros of L-functions, 2002 | arXiv

[3] A. Selberg Contributions to the theory of the Riemann zeta-function, Arch. Math. Naturvid., Volume 48 (1946) no. 5, pp. 89-155

Cité par Sources :

Commentaires - Politique

Ces articles pourraient vous intéresser

On Euler products and multi-variate Gaussians

Dennis A. Hejhal

C. R. Math (2003)

On the horizontal distribution of zeros of linear combinations of Euler products

Dennis A. Hejhal

C. R. Math (2004)

A Lidskii type formula for Dixmier traces

Nurulla A. Azamov; Fyodor A. Sukochev

C. R. Math (2005)