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Izv. RAN. Ser. Mat., 2000, Volume 64, Issue 6, Pages 41–64 (Mi izv311)  

This article is cited in 18 scientific papers (total in 18 papers)

Incomplete Kloosterman sums and their applications

M. A. Korolev


Abstract: We obtain a non-trivial estimate for the upper bound of the absolute value of incomplete Kloosterman sums in which the number of terms is much less than the modulus.

DOI: https://doi.org/10.4213/im311

Full text: PDF file (1394 kB)
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English version:
Izvestiya: Mathematics, 2000, 64:6, 1129–1152

Bibliographic databases:

MSC: 11L05, 11K06, 11L05, 11J54, 11J71
Received: 11.04.2000

Citation: M. A. Korolev, “Incomplete Kloosterman sums and their applications”, Izv. RAN. Ser. Mat., 64:6 (2000), 41–64; Izv. Math., 64:6 (2000), 1129–1152

Citation in format AMSBIB
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\by M.~A.~Korolev
\paper Incomplete Kloosterman sums and their applications
\jour Izv. RAN. Ser. Mat.
\yr 2000
\vol 64
\issue 6
\pages 41--64
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\transl
\jour Izv. Math.
\yr 2000
\vol 64
\issue 6
\pages 1129--1152
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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. Shparlinski I.E., “Bounds of incomplete multiple Kloosterman sums”, Journal of Number Theory, 126:1 (2007), 68–73  crossref  mathscinet  zmath  isi  scopus
    2. Shparlinski I.E., “Distribution of Points on Modular Hyperbolas”, Number Theory: Sailing on the Sea of Number Theory, Series on Number Theory and its Applications, 2, 2007, 155–189  crossref  mathscinet  zmath  isi
    3. M. Z. Garaev, “Estimation of Kloosterman Sums with Primes and Its Application”, Math. Notes, 88:3 (2010), 330–337  mathnet  crossref  crossref  mathscinet  isi
    4. A. A. Karatsuba, “New Estimates of Short Kloosterman Sums”, Math. Notes, 88:3 (2010), 347–359  mathnet  crossref  crossref  mathscinet  isi
    5. M. A. Korolev, “Short Kloosterman Sums with Weights”, Math. Notes, 88:3 (2010), 374–385  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. Wang Yu., Li H., “On s-dimensional incomplete Kloosterman sums”, Journal of Number Theory, 130:7 (2010), 1602–1608  crossref  mathscinet  zmath  isi  scopus
    7. Shparlinski I.E., “Modular Hyperbolas”, Jap. J. Math., 7:2 (2012), 235–294  crossref  mathscinet  zmath  isi  elib  scopus
    8. 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
    9. Bourgain J. Garaev M.Z., “Kloosterman Sums in Residue Rings”, Acta Arith., 164:1 (2014), 43–64  crossref  mathscinet  zmath  isi  scopus
    10. 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
    11. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi  elib
    12. M. A. Korolev, “Metody otsenok korotkikh summ Kloostermana”, Chebyshevskii sb., 17:4 (2016), 79–109  mathnet  crossref  mathscinet  elib
    13. 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
    14. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  isi  elib  elib
    15. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  adsnasa  isi  elib
    16. 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
    17. Drappeau S., Muellner C., “Exponential Sums With Automatic Sequences”, Acta Arith., 185:1 (2018), 81–99  crossref  mathscinet  zmath  isi  scopus
    18. M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170  mathnet  crossref  crossref  isi  elib
  • Известия Российской академии наук. Серия математическая Izvestiya: Mathematics
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