Moscow University Mathematics Bulletin

, Volume 67, Issue 1, pp 23–28 | Cite as

Square exponent of irrationality of ln2

  • A. A. Polyanskii


A new proof of the theorem on the non-quadraticity measure ln 2 is given in the paper.


Prime Number Zeta Function Permutation Group Leninskie Gory Riemannian Zeta Function 
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  1. 1.
    M. Hata, “ℂ2-Saddle Method and Beukers’ Integral,” Trans. Amer. Math. Soc. 352(10), 4557 (2000).MathSciNetzbMATHCrossRefGoogle Scholar
  2. 2.
    R. Marcovecchio, “The Rhin-Viola Method for log 2,” Acta arithm. 139.2, 147 (2009).MathSciNetCrossRefGoogle Scholar
  3. 3.
    G. Rhin and C. Viola, “On a Permutation Group Related to ξ(2),” Acta arithm. 77, 23 (1996).MathSciNetzbMATHGoogle Scholar
  4. 4.
    G. Rhin and C. Viola, “The Group Structure for ξ(3),” Acta arithm. 97, 269 (2001).MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Yu. V. Nesterenko, “Some Remarks on ξ(3),” Matem. Zametki 59(6), 865 (1996).MathSciNetGoogle Scholar
  6. 6.
    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)].Google Scholar
  7. 7.
    E. T. Whittaker and G. N. Watson, A Course of Modern Analysis (Cambridge Univ. Press, 1927; Fizmatgiz, Moscow, 1963).Google Scholar

Copyright information

© Allerton Press, Inc. 2012

Authors and Affiliations

  • A. A. Polyanskii
    • 1
  1. 1.Faculty of Mechanics and MathematicsMoscow State UniversityLeninskie Gory, MoscowRussia

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