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Mat. Sb., 2017, Volume 208, Number 12, Pages 107–123 (Mi msb8801)  

This article is cited in 5 scientific papers (total in 5 papers)

Irreducible solutions of an equation involving reciprocals

S. V. Konyagin, M. A. Korolev

Steklov Mathematical Institute of Russian Academy of Sciences, Moscow

Abstract: An asymptotic formula, with a new estimate for the remainder term, is obtained for the number of solutions of a symmetric Diophantine equation involving reciprocal integers.
Bibliography: 7 titles.

Keywords: reciprocals, Diophantine equations, moments of Kloosterman sums.

Funding Agency Grant Number
Russian Science Foundation 14-50-00005
This work was supported by the Russian Science Foundation under grant no. 14-50-00005.


DOI: https://doi.org/10.4213/sm8801

Full text: PDF file (847 kB)
First page: PDF file
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2017, 208:12, 1818–1834

Bibliographic databases:

Document Type: Article
UDC: 511.33+511.5
MSC: Primary 11D41, 11D72; Secondary 11L05
Received: 21.08.2016 and 20.02.2017

Citation: S. V. Konyagin, M. A. Korolev, “Irreducible solutions of an equation involving reciprocals”, Mat. Sb., 208:12 (2017), 107–123; Sb. Math., 208:12 (2017), 1818–1834

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm8801
  • http://mi.mathnet.ru/eng/msb/v208/i12/p107

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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 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
    2. M. A. Korolev, “On a Diophantine inequality with reciprocals”, Proc. Steklov Inst. Math., 299 (2017), 132–142  mathnet  crossref  crossref  isi  elib  elib
    3. M. A. Korolev, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  adsnasa  isi  elib
    4. 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
    5. 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
  • Математический сборник Sbornik: Mathematics (from 1967)
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