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Mat. Zametki, 2010, Volume 88, Issue 4, Pages 549–564 (Mi mz8686)  

This article is cited in 12 scientific papers (total in 12 papers)

On the Irrationality Exponent of the Number $\ln2$

Yu. V. Nesterenko

M. V. Lomonosov Moscow State University

Abstract: We propose another method of deriving the Marcovecchio estimate for the irrationality measure of the number $\ln2$ following, for the most part, the method of proof of the irrationality of the number $\zeta(3)$ proposed by the author in 1996. The proof uses single complex integrals, the so-called Meyer $G$-functions, and is much simpler than that of Marcovecchio.

Keywords: irrational number, Marcovecchio estimate, irrationality measure, irrationality exponent, Meyer $G$-function, saddle-point method

DOI: https://doi.org/10.4213/mzm8686

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English version:
Mathematical Notes, 2010, 88:4, 530–543

Bibliographic databases:

Document Type: Article
UDC: 511
Received: 03.01.2010
Revised: 15.02.2010

Citation: Yu. V. Nesterenko, “On the Irrationality Exponent of the Number $\ln2$”, Mat. Zametki, 88:4 (2010), 549–564; Math. Notes, 88:4 (2010), 530–543

Citation in format AMSBIB
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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. G. Bashmakova, “Approximation of Values of the Gauss Hypergeometric Function by Rational Fractions”, Math. Notes, 88:6 (2010), 785–797  mathnet  crossref  crossref  mathscinet  isi
    2. A. A. Polyanskii, “Square exponent of irrationality of $\ln 2$”, Moscow University Mathematics Bulletin, 67:1 (2012), 23–28  mathnet  crossref
    3. A. A. Polyanskii, “Quadratic irrationality exponents of certain numbers”, Moscow University Mathematics Bulletin, 68:5 (2013), 237–240  mathnet  crossref  mathscinet
    4. Marcovecchio R., “Multiple Legendre Polynomials in Diophantine Approximation”, Int. J. Number Theory, 10:7 (2014), 1829–1855  crossref  mathscinet  zmath  isi  scopus
    5. Guo Y.-J., Wen Zh.-X., Wu W., “On the Irrationality Exponent of the Regular Paperfolding Numbers”, Linear Alg. Appl., 446 (2014), 237–264  crossref  mathscinet  zmath  isi  elib  scopus
    6. V. A. Androsenko, “Irrationality measure of the number $\frac{\pi}{\sqrt{3}}$”, Izv. Math., 79:1 (2015), 1–17  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    7. V. A. Androsenko, V. Kh. Salikhov, “Symmetrized Version of the Markovecchio Integral in the Theory of Diophantine Approximations”, Math. Notes, 97:4 (2015), 493–501  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    8. Yu. V. Nesterenko, “On Catalan's constant”, Proc. Steklov Inst. Math., 292 (2016), 153–170  mathnet  crossref  crossref  mathscinet  isi  elib
    9. T. Rivoal, “Values of the Beta Function: from Ramanujan's Continued Fraction to Hermite–Padé Approximants”, Proc. Steklov Inst. Math., 298, suppl. 1 (2017), 57–69  mathnet  crossref  crossref  isi  elib
    10. M. Yu. Luchin, V. Kh. Salikhov, “Approximating $\ln 2$ by numbers in the field $\mathbb{Q}(\sqrt{2} )$”, Izv. Math., 82:3 (2018), 549–577  mathnet  crossref  crossref  adsnasa  isi  elib
    11. V. G. Lysov, “O diofantovykh priblizheniyakh proizvedeniya logarifmov”, Preprinty IPM im. M. V. Keldysha, 2018, 158, 20 pp.  mathnet  crossref
    12. A. A. Poljanskij, “On the Irrationality Measures of Certain Numbers. II”, Math. Notes, 103:4 (2018), 626–634  mathnet  crossref  crossref  isi  elib
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