Yu. V. Nesterenko, “A few remarks on $\zeta(3)$”, Mat. Zametki, 59:6 (1996), 865–880; Math. Notes, 59:6 (1996), 625

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Matematicheskie Zametki, 1996, Volume 59, Issue 6, Pages 865–880
DOI: https://doi.org/10.4213/mzm1785 (Mi mzm1785)

This article is cited in 52 scientific papers (total in 53 papers)

A few remarks on

$\zeta(3)$

Yu. V. Nesterenko

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

Full-text PDF (214 kB) Citations (53)

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DOI: https://doi.org/10.4213/mzm1785

Abstract: A new proof of the irrationality of the number

$\zeta(3)$ is proposed. A new decomposition of this number into a continued fraction is found. Recurrence relations are proved for some sequences of Meyer's

$G$ -functions that define a sequence of rational approximations to

$\zeta(3)$ at the point 1.

Received: 29.11.1995

English version:
Mathematical Notes, 1996, Volume 59, Issue 6, Pages 625–636
DOI: https://doi.org/10.1007/BF02307212

Bibliographic databases:

UDC: 511.36

Language: Russian

Citation: Yu. V. Nesterenko, “A few remarks on

$\zeta(3)$ ”, Mat. Zametki, 59:6 (1996), 865–880; Math. Notes, 59:6 (1996), 625–636

Citation in format AMSBIB

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Linking options:

https://www.mathnet.ru/eng/mzm1785

https://doi.org/10.4213/mzm1785

https://www.mathnet.ru/eng/mzm/v59/i6/p865

This publication is cited in the following 53 articles:

Tanguy Rivoal, “Les E-fonctions et G-fonctions de Siegel”, Journées mathématiques X-UPS, 2024, 197
Angelo B. Mingarelli, “Principal Solutions of Recurrence Relations and Irrationality Questions in Number Theory”, Mathematics, 11:2 (2023), 262
Chen Ch.-P., “Asymptotic Results of the Remainders in the Series Representations For the Apery Constant”, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 116:1 (2022), 28
Noriko Hirata-Kohno, Hirata-Kohno Noriko, “Diophantine approximation”, Sugaku Expositions, 34:2 (2021), 205
Marcovecchio R., Zudilin W., “Hypergeometric Rational Approximations to Zeta(4)”, Proc. Edinb. Math. Soc., 63:2 (2020), 374–397
Soria-Lorente A., Berres S., “A Single Parameter Hermite-Pade Series Representation For Apery'S Constant”, Notes Number Theory Discret. Math., 26:3 (2020), 107–134
Arvesu J., Soria-Lorente A., “On Infinitely Many Rational Approximants to Zeta(3)”, Mathematics, 7:12 (2019), 1176
Soria Lorente A., “On Zudilin-Like Rational Approximations to ? (5)”, Notes Number Theory Discret. Math., 24:2 (2018), 104–116
Osburn R., Straub A., Zudilin W., “A Modular Supercongruence For F-6(5): An Apery-Like Story”, Ann. Inst. Fourier, 68:5 (2018), 1987–2004
E. A. Karatsuba, “On One method for constructing a family of approximations of zeta constants by rational fractions”, Problems Inform. Transmission, 51:4 (2015), 378–390
M. Ram Murty, Purusottam Rath, Transcendental Numbers, 2014, 185
M. Ram Murty, Purusottam Rath, Transcendental Numbers, 2014, 75
Pilehrood Kh.H. Pilehrood T.H., “On a Continued Fraction Expansion for Euler's Constant”, J. Number Theory, 133:2 (2013), 769–786
Lagarias J.C., “Euler's Constant: Euler's Work and Modern Developments”, Bull. Amer. Math. Soc., 50:4 (2013), 527–628
Huttner M., “Riemann Beta-Scheme, Monodromy and Diophantine Approximations”, Indag. Math.-New Ser., 23:3 (2012), 522–546
Mortici C., “Estimating the Apery's Constant”, J. Comput. Anal. Appl., 14:2 (2012), 278–282
A. A. Polyanskii, “Square exponent of irrationality of $\ln 2$ ”, Moscow University Mathematics Bulletin, 67:1 (2012), 23–28
Władysław Narkiewicz, Springer Monographs in Mathematics, Rational Number Theory in the 20th Century, 2012, 307
W. Zudilin, “Arithmetic hypergeometric series”, Russian Math. Surveys, 66:2 (2011), 369–420
Gutnik L., “Elementary Proof of Yu. V. Nesterenko Expansion of the Number Zeta(3) in Continued Fraction”, Advances in Difference Equations, 2010, 143521

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

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