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.

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Copyright information

© Allerton Press, Inc. 2013

Authors and Affiliations

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

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