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

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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. Blomer^a, É. Fouvry^b, E. Kowalski^c, Ph. Michel^d, Dj. Milićević^ef

^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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Linking options:

https://www.mathnet.ru/eng/tm3792

https://doi.org/10.1134/S0371968517010022

https://www.mathnet.ru/eng/tm/v296/p24

This publication is cited in the following 18 articles:

Christian Bagshaw, “Bilinear forms with Kloosterman and Gauss sums in function fields”, Finite Fields and Their Applications, 94 (2024), 102356
Houcein El Abdalaoui, Igor E. Shparlinski, Raphael S. Steiner, “Chowla and Sarnak conjectures for Kloosterman sums”, Mathematische Nachrichten, 297:1 (2024), 209
Peng Gao, “Bounds for moments of Dirichlet L-functions to a fixed modulus”, Math. Z., 307:4 (2024)
Igor E. Shparlinski, “Sums of multidimensional Kloosterman sums”, Period Math Hung, 2024
Nilanjan Bag, Igor E. Shparlinski, “Bounds on bilinear sums of Kloosterman sums”, Journal of Number Theory, 242 (2023), 102
Xiaosheng Wu, “The fourth moment of Dirichlet L-functions along the critical line”, Forum Mathematicum, 35:5 (2023), 1347
Xiaosheng Wu, “The fourth moment of Dirichlet L-functions at the central value”, Math. Ann., 387:3-4 (2023), 1199
Bryce Kerr, Igor E. Shparlinski, Xiaosheng Wu, Ping Xi, “Bounds on bilinear forms with Kloosterman sums”, Journal of London Math Soc, 108:2 (2023), 578
Topacogullari B., “The Fourth Moment of Individual Dirichletl-Functions on the Critical Line”, Math. Z., 298:1-2 (2021), 577–624
M. Korolev, I. Shparlinski, “Sums of algebraic trace functions twisted by arithmetic functions”, Pac. J. Math., 304:2 (2020), 505–522
W. Banks, I. Shparlinski, “Congruences with intervals and arbitrary sets”, Arch. Math., 114:5 (2020), 527–539
A. Dunn, A. Zaharescu, “Sums of Kloosterman sums over primes in an arithmetic progression”, Q. J. Math., 70:1 (2019), 319–342
I. E. Shparlinski, “On sums of Kloosterman and Gauss sums”, Trans. Am. Math. Soc., 371:12 (2019), 8679–8697
K. Liu, I. E. Shparlinski, T. Zhang, “Cancellations between Kloosterman sums modulo a prime power with prime arguments”, Mathematika, 65:3 (2019), 475–487
S. Macourt, I. E. Shparlinski, “Double sums of Kloosterman sums in finite fields”, Finite Fields their Appl., 60 (2019), UNSP 101575
R. Zacharias, “Mollification of the Fourth Moment of Dirichlet l-functions”, Acta Arith., 191:3 (2019), 201–257
K. Liu, I. E. Shparlinski, T. Zhang, “Bilinear forms with exponential sums with binomials”, J. Number Theory, 188 (2018), 172–185
I. E. Shparlinski, “Trilinear forms with double Kloosterman sums”, Int. J. Number Theory, 14:8 (2018), 2195–2203

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

Труды Математического института имени В. А. Стеклова

Proceedings of the Steklov Institute of Mathematics

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