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Tr. Mat. Inst. Steklova, 2017, Volume 296, Pages 163–180 (Mi tm3785)  

This article is cited in 4 scientific papers (total in 4 papers)

Generalized Kloosterman sum with primes

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: The work is devoted to generalized Kloosterman sums modulo a prime, i.e., trigonometric sums of the form $\sum _{p\le x}\exp \{2\pi i (a\overline {p} {+} F_k(p))/q\}$ and $\sum _{n\le x}\mu (n)\exp \{2\pi i (a\overline {n} {+} F_k(n))/q\}$, where $q$ is a prime number, $(a,q)=1$, $m\overline {m}\equiv 1\pmod q$, $F_k(u)$ is a polynomial of degree $k\ge 2$ with integer coefficients, and $p$ runs over prime numbers. An upper estimate with a power saving is obtained for the absolute values of such sums for $x\ge q^{1/2+\varepsilon }$.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968517010137

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 296, 154–171

Bibliographic databases:

Document Type: Article
UDC: 511.321
Received: April 13, 2016

Citation: M. A. Korolev, “Generalized Kloosterman sum with primes”, Analytic and combinatorial number theory, Collected papers. On the occasion of the 125th anniversary of the birth of Academician Ivan Matveevich Vinogradov, Tr. Mat. Inst. Steklova, 296, MAIK Nauka/Interperiodica, Moscow, 2017, 163–180; Proc. Steklov Inst. Math., 296 (2017), 154–171

Citation in format AMSBIB
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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  adsnasa  isi  elib
    2. M. A. Korolev, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Math. Notes, 103:5 (2018), 761–768  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    3. M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Sb. Math., 209:5 (2018), 652–659  mathnet  crossref  crossref  adsnasa  isi  elib
    4. M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170  mathnet  crossref  crossref  isi  elib
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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