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

Presented by: 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.

Abstract
Résumé

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 ${Re (s) = \frac{1}{2}}$ .

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 ${Re (s) = \frac{1}{2}}$ .

Received: 2004-03-02
Accepted: 2004-03-09
Published online: 2004-04-14

DOI: 10.1016/j.crma.2004.03.022

Author's affiliations:

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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     title = {On the horizontal distribution of zeros of linear combinations of {Euler} products},
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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/

References
Cited by

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[5] D. Hejhal On Euler products and multivariate Gaussians, C. R. Acad. Sci. Paris, Ser. I, Volume 337 (2003), pp. 223-226

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