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Zero-free regions for Dirichlet series

Authors: C. Delaunay, E. Fricain, E. Mosaki and O. Robert
Journal: Trans. Amer. Math. Soc. 365 (2013), 3227-3253
MSC (2010): Primary 11M26, 30H10
Published electronically: September 19, 2012
MathSciNet review: 3034464
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Abstract: In this paper, we are interested in explicit zero-free discs for some Dirichlet series and we also study a general Beurling-Nyman criterion for $ L$-functions. Our results generalize and improve previous results obtained by N. Nikolski and by A. de Roton. As a concrete application, we get, for example, a Beurling-Nyman type criterion for the Siegel zero problem.

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Additional Information

C. Delaunay
Affiliation: Université de Franche-Comté, Laboratoire de Mathématiques de Besançon, CNRS UMR 6623, 16, route de Gray, F-25030 Besançon, France

E. Fricain
Affiliation: Laboratoire Paul Painlevé, UMR no. 8524, Bât. M2, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France

E. Mosaki
Affiliation: Université de Lyon, Université Lyon 1, Institut Camille Jordan CNRS UMR 5208, 43, boulevard du 11 Novembre 1918, F-69622 Villeurbanne, France

O. Robert
Affiliation: Université de Lyon, Université de Saint-Etienne, LaMUSE (EA 3989), 23, rue du Dr P. Michelon, F-42000, Saint-Etienne, France

Keywords: Dirichlet series, Beurling–Nyman criterion, Hardy spaces, zeros of $L$-functions.
Received by editor(s): January 6, 2011
Received by editor(s) in revised form: September 21, 2011, and October 28, 2011
Published electronically: September 19, 2012
Additional Notes: This work was supported by the ANR project no. 07-BLAN-0248 “ALGOL”, the ANR project no. 09-BLAN-005801 “FRAB” and the ANR project no. 08-BLAN-0257 “PEPR”.
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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