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Matematicheskie Zametki, 2018, Volume 103, Issue 5, Pages 720–729
DOI: https://doi.org/10.4213/mzm11878 (Mi mzm11878) 		 
This article is cited in 4 scientific papers (total in 4 papers)

Elementary Proof of an Estimate for Kloosterman Sums with Primes

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
Full-text PDF (463 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm11878
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.
Received: 05.12.2017
English version:
Mathematical Notes, 2018, Volume 103, Issue 5, Pages 761–768
DOI: https://doi.org/10.1134/S0001434618050085
Bibliographic databases:
Document Type: Article
UDC: 517
Language: Russian
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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