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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2017, Volume 296, Pages 24–35
DOI: https://doi.org/10.1134/S0371968517010022 (Mi tm3792) 		 
This article is cited in 18 scientific papers (total in 18 papers)

Some applications of smooth bilinear forms with Kloosterman sums

V. Blomera, É. Fouvryb, E. Kowalskic, Ph. Micheld, Dj. Milićevićef

a Mathematisches Institut, Universität Göttingen, Göttingen, Germany
b Laboratoire de Mathématiques d'Orsay, Université Paris–Saclay, Orsay Cedex, France
c Department of Mathematics, ETH Zürich, Zürich, Switzerland
d Chaire TAN, École Polytechnique Fédérale de Lausanne, Lausanne, Switzerland
e Department of Mathematics, Bryn Mawr College, Bryn Mawr, PA, USA
f Max-Planck-Institut für Mathematik, Bonn, Germany
Full-text PDF (237 kB) Citations (18)
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DOI: https://doi.org/10.1134/S0371968517010022
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.
Funding agency Grant number
Swiss National Science Foundation 200021-137488
European Research Council 228304
DFG–SNF 200021L_153647
Australian Research Council DP130100674
National Science Foundation DMS-1503629
Volkswagen Foundation
Eidgenösische Technische Hochschule Zürich
École Polytechnique Fédérale de Lausanne
V.B. was partially supported by the Volkswagen Foundation. É.F. thanks ETH Zürich and EPF Lausanne for financial support. Ph.M. was partially supported by the SNF (grant 200021-137488) and the ERC (Advanced Research Grant 228304). V.B., Ph.M. and E.K. were also partially supported by a DFG–SNF lead agency program grant (grant 200021L_153647). D.M. was partially supported by the NSF (grant DMS-1503629) and ARC (through grant DP130100674).
Received: May 6, 2016
English version:
Proceedings of the Steklov Institute of Mathematics, 2017, Volume 296, Pages 18–29
DOI: https://doi.org/10.1134/S0081543817010023
Bibliographic databases:
Document Type: Article
UDC: 511.321
Language: Russian
Citation: V. Blomer, É. Fouvry, E. Kowalski, Ph. Michel, Dj. Milićević, “Some applications of smooth bilinear forms with Kloosterman sums”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Trudy Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 24–35; Proc. Steklov Inst. Math., 296 (2017), 18–29
Citation in format AMSBIB
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\paper Some applications of smooth bilinear forms with Kloosterman sums
\inbook Analytic and combinatorial number theory
\bookinfo Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov
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\vol 296
\pages 24--35
\publ MAIK Nauka/Interperiodica
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    • This publication is cited in the following 18 articles:
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
     
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