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Mat. Zametki, 2016, Volume 100, Issue 6, Pages 838–846 (Mi mz11048)  

This article is cited in 7 scientific papers (total in 7 papers)

On Short Kloosterman Sums Modulo a Prime

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences

Abstract: Using the Karatsuba method, we obtain new estimates for Kloosterman sums modulo a prime, which, under certain constraints on the number of summands, are sharper than similar estimates found earlier.

Keywords: Kloosterman sum, Karatsuba method, inverse quantities.

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/mzm11048

Full text: PDF file (440 kB)
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English version:
Mathematical Notes, 2016, 100:6, 820–827

Bibliographic databases:

Document Type: Article
UDC: 517
Received: 22.12.2015
Revised: 27.08.2016

Citation: M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Mat. Zametki, 100:6 (2016), 838–846; Math. Notes, 100:6 (2016), 820–827

Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm11048
  • http://mi.mathnet.ru/eng/mz/v100/i6/p838

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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, “Metody otsenok korotkikh summ Kloostermana”, Chebyshevskii sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
    2. 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
    3. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  isi  elib  elib
    4. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  adsnasa  isi  elib
    5. 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
    6. 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
    7. M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170  mathnet  crossref  crossref  isi  elib
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