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Mat. Zametki, 2010, Volume 88, Issue 3, Pages 415–427 (Mi mz8814)  

This article is cited in 10 scientific papers (total in 10 papers)

Short Kloosterman Sums with Weights

M. A. Korolev

Steklov Mathematical Institute, Russian Academy of Sciences

Abstract: We obtain a new estimate for Kloosterman sums with weights in which the number of summands is significantly less than any arbitrarily small fixed power of the modulus.

Keywords: Kloosterman sum with weight, prime number, Euler function, Möbius function, square-free number

DOI: https://doi.org/10.4213/mzm8814

Full text: PDF file (482 kB)
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English version:
Mathematical Notes, 2010, 88:3, 374–385

Bibliographic databases:

UDC: 511.33
Received: 20.08.2009

Citation: M. A. Korolev, “Short Kloosterman Sums with Weights”, Mat. Zametki, 88:3 (2010), 415–427; Math. Notes, 88:3 (2010), 374–385

Citation in format AMSBIB
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\paper Short Kloosterman Sums with Weights
\jour Mat. Zametki
\yr 2010
\vol 88
\issue 3
\pages 415--427
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\transl
\jour Math. Notes
\yr 2010
\vol 88
\issue 3
\pages 374--385
\crossref{https://doi.org/10.1134/S0001434610090105}
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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. A. Karatsuba, “New Estimates of Short Kloosterman Sums”, Math. Notes, 88:3 (2010), 347–359  mathnet  crossref  crossref  mathscinet  isi
    2. J. Bourgain, M. Z. Garaev, “Sumsets of reciprocals in prime fields and multilinear Kloosterman sums”, Izv. Math., 78:4 (2014), 656–707  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    3. Bourgain J. Garaev M.Z., “Kloosterman Sums in Residue Rings”, Acta Arith., 164:1 (2014), 43–64  crossref  mathscinet  zmath  isi  scopus
    4. M. A. Korolev, “Karatsuba's method for estimating Kloosterman sums”, Sb. Math., 207:8 (2016), 1142–1158  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi  elib
    6. M. A. Korolev, “Metody otsenok korotkikh summ Kloostermana”, Chebyshevskii sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
    7. 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
    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, “Elementary Proof of an Estimate for Kloosterman Sums with Primes”, Math. Notes, 103:5 (2018), 761–768  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    10. 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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