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Mat. Zametki, 2018, Volume 103, Issue 5, Pages 720–729 (Mi mz11878)  

This article is cited in 1 scientific paper (total in 1 paper)

Elementary Proof of an Estimate for Kloosterman Sums with Primes

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: A new elementary proof of an estimate for incomplete Kloosterman sums modulo a prime $q$ is obtained. Along with Bourgain's 2005 estimate of the double Kloosterman sum of a special form, it leads to an elementary derivation of an estimate for Kloosterman sums with primes for the case in which the length of the sum is of order $q^{0.5+\varepsilon}$, where $\varepsilon$ is an arbitrarily small fixed number.

Keywords: Kloosterman sum, primes.

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


DOI: https://doi.org/10.4213/mzm11878

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English version:
Mathematical Notes, 2018, 103:5, 761–768

Bibliographic databases:

Document Type: Article
UDC: 517
Received: 05.12.2017

Citation: M. A. Korolev, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Mat. Zametki, 103:5 (2018), 720–729; Math. Notes, 103:5 (2018), 761–768

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11878
  • http://mi.mathnet.ru/eng/mz/v103/i5/p720

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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, “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
  • Математические заметки Mathematical Notes
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