Comptes Rendus
no. 10
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. Hejhal1, 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.

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)=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)=1 2}.

Reçu le :
Accepté le :
Publié le :
DOI : 10.1016/j.crma.2004.03.022
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/

[1] A. Beurling On functions with a spectral gap, The Collected Works of Arne Beurling, vol. 2, Birkhäuser, 1989, pp. 370-372

[2] E. Bombieri; D. Hejhal On the distribution of zeros of linear combinations of Euler products, Duke Math. J., Volume 80 (1995), pp. 821-862

[3] L. Carleson Selected Problems on Exceptional Sets, Van Nostrand, 1967

[4] D. Hejhal On a result of Selberg concerning zeros of linear combinations of L-functions, Intern. Math. Res. Notices (2000), pp. 551-577

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

[6] A. Selberg Old and new conjectures and results about a class of Dirichlet series, Collected Papers, vol. 2, Springer-Verlag, 1991, pp. 47-63

[7] E. Titchmarsh Theory of Functions, Oxford University Press, 1939

[8] E. Titchmarsh The Theory of the Riemann Zeta-Function, Oxford Univsersity Press, 1951

[9] J. Vaaler Some extremal functions in Fourier analysis, Bull. Amer. Math. Soc. (N.S.), Volume 12 (1985), pp. 183-216

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