[Statisiques linéaires pour les zéros de la fonction zêta de Riemann]
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.
Accepté le :
Publié le :
@article{CRMATH_2002__335_8_667_0,
author = {Hughes, Chris and Rudnick, Ze\'ev},
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},
url = {http://archive.numdam.org/articles/10.1016/S1631-073X(02)02541-4/}
}
TY - JOUR AU - Hughes, Chris AU - Rudnick, Zeév 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 UR - http://archive.numdam.org/articles/10.1016/S1631-073X(02)02541-4/ DO - 10.1016/S1631-073X(02)02541-4 LA - en ID - CRMATH_2002__335_8_667_0 ER -
%0 Journal Article %A Hughes, Chris %A Rudnick, Zeév %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 %U http://archive.numdam.org/articles/10.1016/S1631-073X(02)02541-4/ %R 10.1016/S1631-073X(02)02541-4 %G en %F CRMATH_2002__335_8_667_0
Hughes, Chris; Rudnick, Zeév. Linear statistics for zeros of Riemann's zeta function. Comptes Rendus. Mathématique, Tome 335 (2002) no. 8, pp. 667-670. doi : 10.1016/S1631-073X(02)02541-4. http://archive.numdam.org/articles/10.1016/S1631-073X(02)02541-4/
[1] Explicit formulas and oscillations (Hejhal, D.A.; Friedman, J.; Gutzwiller, M.C.; Odlyzko, A.M., eds.), Emerging Applications of Number Theory, Springer, 1999, pp. 219-267
[2] Linear statistics of low-lying zeros of L-functions, 2002 | arXiv
[3] Contributions to the theory of the Riemann zeta-function, Arch. Math. Naturvid., Volume 48 (1946) no. 5, pp. 89-155
Cité par Sources :
