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Tr. Mat. Inst. Steklova, 2017, Volume 299, Pages 144–154 (Mi tm3847)  

This article is cited in 4 scientific papers (total in 4 papers)

On a Diophantine inequality with reciprocals

M. A. Korolev

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

Abstract: A sharpened lower bound is obtained for the number of solutions to an inequality of the form $\alpha \le \{(a\overline {n}+bn)/q\}<\beta $, $1\le n\le N$, where $q$ is a sufficiently large prime number, $a$ and $b$ are integers with $(ab,q)=1$, $n\overline {n}\equiv 1 \pmod q$, and $0\le \alpha <\beta \le 1$. The length $N$ of the range of the variable $n$ is of order $q^\varepsilon $, where $\varepsilon >0$ is an arbitrarily small fixed number.

Funding Agency Grant Number
Russian Science Foundation 14-11-00433
This work is supported by the Russian Science Foundation under grant 14-11-00433.


DOI: https://doi.org/10.1134/S0371968517040094

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English version:
Proceedings of the Steklov Institute of Mathematics, 2017, 299, 132–142

Bibliographic databases:

Document Type: Article
UDC: 511.321
Received: April 10, 2017

Citation: M. A. Korolev, “On a Diophantine inequality with reciprocals”, Analytic number theory, On the occasion of the 80th anniversary of the birth of Anatolii Alekseevich Karatsuba, Tr. Mat. Inst. Steklova, 299, MAIK Nauka/Interperiodica, Moscow, 2017, 144–154; Proc. Steklov Inst. Math., 299 (2017), 132–142

Citation in format AMSBIB
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\serial Tr. Mat. Inst. Steklova
\yr 2017
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\pages 144--154
\publ MAIK Nauka/Interperiodica
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  • https://doi.org/10.1134/S0371968517040094
  • http://mi.mathnet.ru/eng/tm/v299/p144

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    Citing articles on Google Scholar: Russian citations, English citations
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    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, “Kloosterman sums with multiplicative coefficients”, Izv. Math., 82:4 (2018), 647–661  mathnet  crossref  crossref  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, “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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