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Tr. Mat. Inst. Steklova, 2016, Volume 294, Pages 76–86 (Mi tm3732)  

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

On a symmetric diophantine equation with reciprocals

S. V. Konyagin, M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, ul. Gubkina 8, Moscow, 119991 Russia

Abstract: An asymptotic formula is obtained for the number of solutions to a symmetric Diophantine equation with reciprocals, and its applications to problems related to the distribution of values of short Kloosterman sums are presented.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work is supported by the Russian Science Foundation under grant 14-50-00005.


DOI: https://doi.org/10.1134/S0371968516030043

Full text: PDF file (195 kB)
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English version:
Proceedings of the Steklov Institute of Mathematics, 2016, 294, 67–77

Bibliographic databases:

Document Type: Article
UDC: 511.5+511.321
Received: April 13, 2016

Citation: S. V. Konyagin, M. A. Korolev, “On a symmetric diophantine equation with reciprocals”, Modern problems of mathematics, mechanics, and mathematical physics. II, Collected papers, Tr. Mat. Inst. Steklova, 294, MAIK Nauka/Interperiodica, Moscow, 2016, 76–86; Proc. Steklov Inst. Math., 294 (2016), 67–77

Citation in format AMSBIB
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Linking options:
  • http://mi.mathnet.ru/eng/tm3732
  • https://doi.org/10.1134/S0371968516030043
  • http://mi.mathnet.ru/eng/tm/v294/p76

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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. M. A. Korolev, “On Short Kloosterman Sums Modulo a Prime”, Math. Notes, 100:6 (2016), 820–827  mathnet  crossref  crossref  mathscinet  isi  elib
    2. S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Sb. Math., 208:12 (2017), 1818–1834  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    3. 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
    4. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  isi  elib  elib
    5. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  adsnasa  isi  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
  • Труды Математического института им. В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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