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Mat. Sb., 2018, Volume 209, Number 5, Pages 54–61 (Mi msb8939)  

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

New estimate for a Kloosterman sum with primes for a composite modulus

M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: For an arbitrary composite modulus $q$ a bound is obtained for a short Kloosterman sum with primes whose length exceeds $q^{7/10+\varepsilon}$. This bound improves the previous result by Fouvry and Shparlinski, which holds for sums of length at least $q^{3/4+\varepsilon}$.
Bibliography: 23 titles.

Keywords: Kloosterman sums, reciprocals for a given modulus, prime numbers, composite moduli.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
This work was supported by the Russian Science Foundation under grant no. 14-11-00433.


DOI: https://doi.org/10.4213/sm8939

Full text: PDF file (560 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2018, 209:5, 652–659

Bibliographic databases:

UDC: 511.33
MSC: 11L05
Received: 10.03.2017 and 14.08.2017

Citation: M. A. Korolev, “New estimate for a Kloosterman sum with primes for a composite modulus”, Mat. Sb., 209:5 (2018), 54–61; Sb. Math., 209:5 (2018), 652–659

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8939
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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. Munsch M., Shparlinski I.E., “On Smooth Square-Free Numbers in Arithmetic Progressions”, J. Lond. Math. Soc.-Second Ser.  crossref  isi
    2. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. 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
    4. M. A. Korolev, “Divisors of a quadratic form with primes”, Proc. Steklov Inst. Math., 303 (2018), 154–170  mathnet  crossref  crossref  mathscinet  isi  elib
    5. M. A. Korolev, “Short Kloosterman Sums with Primes”, Math. Notes, 106:1 (2019), 89–97  mathnet  crossref  crossref  mathscinet  isi  elib
    6. M. A. Korolev, M. E. Changa, “New Estimate for Kloosterman Sums with Primes”, Math. Notes, 108:1 (2020), 87–93  mathnet  crossref  crossref  mathscinet  isi  elib
    7. M. A. Korolev, “Kloosterman sums with primes and the solvability of one congruence with inverse residues — II”, Chebyshevskii sb., 21:1 (2020), 221–232  mathnet  crossref  mathscinet
    8. M. A. Korolev, “Kloosterman sums over primes of composite moduli”, Res. Number Theory, 6:2 (2020), 24  crossref  mathscinet  isi
    9. M. A. Korolev, “Kloosterman Sums with Primes and Solvability of a Congruence with Inverse Residues”, Proc. Steklov Inst. Math., 314 (2021), 96–126  mathnet  crossref  crossref  isi
  • Математический сборник Sbornik: Mathematics (from 1967)
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