Zero-free regions for Dirichlet series
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- by C. Delaunay, E. Fricain, E. Mosaki and O. Robert PDF
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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.References
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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
- Email: christophe.delaunay@univ-fcomte.fr
- E. Fricain
- Affiliation: Laboratoire Paul Painlevé, UMR no. 8524, Bât. M2, Université de Lille 1, 59655 Villeneuve d’Ascq Cedex, France
- MR Author ID: 648628
- Email: fricain@math.univ-lille1.fr
- 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
- Email: mosaki@math.univ-lyon1.fr
- O. Robert
- Affiliation: Université de Lyon, Université de Saint-Etienne, LaMUSE (EA 3989), 23, rue du Dr P. Michelon, F-42000, Saint-Etienne, France
- MR Author ID: 663774
- Email: olivier.robert@univ-st-etienne.fr
- 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”.
- © Copyright 2012
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 365 (2013), 3227-3253
- MSC (2010): Primary 11M26, 30H10
- DOI: https://doi.org/10.1090/S0002-9947-2012-05735-7
- MathSciNet review: 3034464