Yu. A. Pupyrev, “Effectivization of a Lower Bound for $\|(4/3)^k\|$”, Mat. Zametki, 85:6 (2009), 927–935; Math. Notes, 85:6 (2009), 877

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Matematicheskie Zametki, 2009, Volume 85, Issue 6, Pages 927–935
DOI: https://doi.org/10.4213/mzm6192 (Mi mzm6192)

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

Effectivization of a Lower Bound for

$\|(4/3)^k\|$

Yu. A. Pupyrev

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

Full-text PDF (474 kB) Citations (5)

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DOI: https://doi.org/10.4213/mzm6192

Abstract: We obtain an effective lower bound for

$\|(4/3)^k\|$ , where

$\|\cdot\|$ denotes the distance to the nearest integer.

Keywords: Waring's problem, effective lower bound, effective constant, Beukers estimate, Padé approximation, Stirling's formula.

Received: 15.09.2008
Revised: 20.02.2009

English version:
Mathematical Notes, 2009, Volume 85, Issue 6, Pages 877–885
DOI: https://doi.org/10.1134/S0001434609050289

Bibliographic databases:

UDC: 511.3

Language: Russian

Citation: Yu. A. Pupyrev, “Effectivization of a Lower Bound for

$\|(4/3)^k\|$ ”, Mat. Zametki, 85:6 (2009), 927–935; Math. Notes, 85:6 (2009), 877–885

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm6192

https://doi.org/10.4213/mzm6192

https://www.mathnet.ru/eng/mzm/v85/i6/p927

This publication is cited in the following 5 articles:

Barnea T., “The Riemann Zeta Function and the Fractional Part of Rational Powers”, J. Integer Seq., 22:3 (2019), 19.3.6
Pupyrev Yu., “On a Lower Bound For $\|(4/3)^k$”, Int. J. Number Theory, 11:1 (2015), 299–309
Władysław Narkiewicz, Springer Monographs in Mathematics, Rational Number Theory in the 20th Century, 2012, 195
W. Zudilin, “Arithmetic hypergeometric series”, Russian Math. Surveys, 66:2 (2011), 369–420
Yu. A. Pupyrev, “Rational Approximations of the Number $\sqrt[3]{3}$”, Math. Notes, 86:5 (2009), 693–703

Citing articles in Google Scholar: Russian citations, English citations
Related articles in Google Scholar: Russian articles, English articles

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Full-text PDF :	201
References:	80
First page:	6

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