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

Dennis A. Hejhal

doi:10.1016/j.crma.2004.03.022

Number Theory

On the horizontal distribution of zeros of linear combinations of Euler products
[Sur la distribution horizontale des zéros de combinaisons linéaires des produits eulériens]

Présenté par : Alain Connes

Dennis A. Hejhal ^1,²

¹ Department of Mathematics, Box 480, Uppsala University, 75106 Uppsala, Sweden
² School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 755-758.

Résumé
Abstract

Nous étudions certaines séries de Dirichlet naturelles qui satisfont une équation fonctionelle ainsi qu'une fonction dénombrant leurs zéros dans certains domaines rectangulaires proches de la droite critique ${Re (s) = \frac{1}{2}}$ .

We investigate the behavior of the zero counting function of certain natural Dirichlet series with functional equation in the immediate vicinity of the critical line ${Re (s) = \frac{1}{2}}$ .

Reçu le : 2004-03-02
Accepté le : 2004-03-09
Publié le : 2004-04-14

DOI : 10.1016/j.crma.2004.03.022

Affiliations des auteurs :

Dennis A. Hejhal ^{1, 2}

¹ Department of Mathematics, Box 480, Uppsala University, 75106 Uppsala, Sweden
² School of Mathematics, University of Minnesota, Minneapolis, MN 55455, USA

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Dennis A. Hejhal. On the horizontal distribution of zeros of linear combinations of Euler products. Comptes Rendus. Mathématique, Volume 338 (2004) no. 10, pp. 755-758. doi : 10.1016/j.crma.2004.03.022. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/j.crma.2004.03.022/

Bibliographie
Cité par

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Youness Lamzouri; Yoonbok Lee The number of zeros of linear combinations of L-functions near the critical line, Journal d'Analyse Mathématique, Volume 152 (2024) no. 2, p. 669 | DOI:10.1007/s11854-023-0307-y
Haseo Ki; Yasushi Komori; Masatoshi Suzuki On the zeros of Weng zeta functions for Chevalley groups, Manuscripta Mathematica, Volume 148 (2015) no. 1-2, p. 119 | DOI:10.1007/s00229-015-0736-8
Dennis A. Hejhal Turing: a bit off the beaten path, The Mathematical Intelligencer, Volume 29 (2007) no. 1, p. 27 | DOI:10.1007/bf02984757

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