Email this article Some applications of smooth bilinear forms with Kloosterman sums
- Authors: Blomer V.1, Fouvry É.2, Kowalski E.3, Michel P.4, Milićević D.3,5
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Affiliations:
- Mathematisches Institut
- Laboratoire de Mathématiques d’Orsay
- Department of Mathematics
- Chaire TAN
- Max-Planck-Institut für Mathematik
- Issue: Vol 296, No 1 (2017)
- Pages: 18-29
- Section: Article
- URL: https://journals.rcsi.science/0081-5438/article/view/174193
- DOI: https://doi.org/10.1134/S0081543817010023
- ID: 174193
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Abstract
We revisit a recent bound of I. Shparlinski and T. Zhang on bilinear forms with Kloosterman sums, and prove an extension for correlation sums of Kloosterman sums against Fourier coefficients of modular forms. We use these bounds to improve on earlier results on sums of Kloosterman sums along the primes and on the error term of the fourth moment of Dirichlet L-functions.
About the authors
Valentin Blomer
Mathematisches Institut
Email: dmilicevic@brynmawr.edu
Germany, Bunsenstr. 3-5, Göttingen, D-37073
Étienne Fouvry
Laboratoire de Mathématiques d’Orsay
Email: dmilicevic@brynmawr.edu
France, Orsay Cedex, F-91405
Emmanuel Kowalski
Department of Mathematics
Email: dmilicevic@brynmawr.edu
Switzerland, Rämistrasse 101, Zürich, CH-8092
Philippe Michel
Chaire TAN
Email: dmilicevic@brynmawr.edu
Switzerland, Lausanne, CH-1015
Djordje Milićević
Department of Mathematics; Max-Planck-Institut für Mathematik
Author for correspondence.
Email: dmilicevic@brynmawr.edu
United States, 101 North Merion Ave., Bryn Mawr, PA, 19010-2899; Vivatsgasse 7, Bonn, D-53111
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