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Sbornik: Mathematics, 2016, Volume 207, Issue 8, Pages 1142–1158
DOI: https://doi.org/10.1070/SM8648 (Mi sm8648) 		 
This article is cited in 16 scientific papers (total in 16 papers)

Karatsuba's method for estimating Kloosterman sums

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow
English version PDF (493 kB) Citations (16)
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DOI: https://doi.org/10.1070/SM8648
Abstract: Using Karatsuba's method, we obtain estimates for Kloosterman sums modulo a prime, in which the number of terms is less than an arbitrarily small fixed power of the modulus. These bounds refine similar results obtained earlier by Bourgain and Garaev.
Bibliography: 16 titles.
Keywords: short Kloosterman sums, Karatsuba's method, inverse residues.
Funding agency Grant number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation (grant no. 14-50-00005).
Received: 09.12.2015 and 06.04.2016
Russian version:
Matematicheskii Sbornik, 2016, Volume 207, Number 8, Pages 117–134
DOI: https://doi.org/10.4213/sm8648
Bibliographic databases:
Document Type: Article
UDC: 511.33
MSC: 11L05
Language: English
Original paper language: Russian
Citation: M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Mat. Sb., 207:8 (2016), 117–134; Sb. Math., 207:8 (2016), 1142–1158
Citation in format AMSBIB
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    Russian version PDF:118
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    References:54
    First page:38
     
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