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Mat. Sb., 2016, Volume 207, Number 8, Pages 117–134 (Mi msb8648)  

This article is cited in 9 scientific papers (total in 9 papers)

Karatsuba's method for estimating Kloosterman sums

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

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).


DOI: https://doi.org/10.4213/sm8648

Full text: PDF file (540 kB)
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English version:
Sbornik: Mathematics, 2016, 207:8, 1142–1158

Bibliographic databases:

Document Type: Article
UDC: 511.33
MSC: 11L05
Received: 09.12.2015 and 06.04.2016

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

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  • https://doi.org/10.4213/sm8648
  • http://mi.mathnet.ru/eng/msb/v207/i8/p117

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

    Related presentations:

    This publication is cited in the following articles:
    1. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi  elib
    2. M. A. Korolev, “Metody otsenok korotkikh summ Kloostermana”, Chebyshevskii sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
    3. K. Gong, C. Jia, M. A. Korolev, “Shifted character sums with multiplicative coefficients, II”, J. Number Theory, 178 (2017), 31–39  crossref  mathscinet  zmath  isi  elib  scopus
    4. M. A. Korolev, “On Anatolii Alekseevich Karatsuba's works written in the 1990s and 2000s”, Proc. Steklov Inst. Math., 299 (2017), 1–43  mathnet  crossref  crossref  isi  elib  elib
    5. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  isi  elib  elib
    6. 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
    7. 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
    8. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  adsnasa  isi  elib
    9. M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170  mathnet  crossref  crossref  isi  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
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