Advertisement

Moscow University Mathematics Bulletin

, Volume 68, Issue 5, pp 237–240 | Cite as

Quadratic irrationality exponents of certain numbers

  • A. A. Polyanskii
Article

Abstract

The paper presents upper estimates for the non-quadraticity measure of the numbers \(\sqrt {2k + 1} \ln ((k + 1 - \sqrt {2k + 1} /k)\) and \(\sqrt {2k - 1} arctg(\sqrt {2k - 1} /(k - 1))\), where k ∈ ℕ. In particular, the upper estimate for the non-quadraticity measure of ln 2 is improved.

Keywords

Quadratic Irrationality Irrationality Exponent 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    M. Hata, “ℂ2-Saddle Method and Beukers’ Integral,” Trans. Amer. Math. Soc. 352(10), 4557 (2000).MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    R. Marcovecchio, “The Rhin-Viola Method for log2,” Acta Arithm. 139(2), 147 (2009).MathSciNetCrossRefzbMATHGoogle Scholar
  3. 3.
    A. A. Polyanskii, “Quadratic Exponent of Irrationality of ln 2,” Vestn. Mosk. Univ., Matem. Mekhan., No 1, 25 (2012).Google Scholar
  4. 4.
    Yu. V. Nesterenko, “On the Irrationality Exponent of the Number ln 2,” Matem. Zametki 88(4), 549 (2010) [Math. Notes 88 (3–4), 530 (2010)].MathSciNetCrossRefGoogle Scholar
  5. 5.
    M. G. Bashmakova, “Estimates for the Exponent of Irrationality for Certain Numbers,” Moscow J. Comb, and Number Theory 1(1), 67 (2011).MathSciNetzbMATHGoogle Scholar
  6. 6.
    A. Polyanskii, “On the Irrationality Measure of Certain Numbers,” Moscow J. Comb, and Number Theory 1(4), 80 (2011).MathSciNetzbMATHGoogle Scholar

Copyright information

© Allerton Press, Inc. 2013

Authors and Affiliations

  • A. A. Polyanskii
    • 1
  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityMoscowRussia

Personalised recommendations