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Mathematische Zeitschrift

, Volume 254, Issue 2, pp 299–313 | Cite as

Irrationality of certain numbers that contain values of the di- and trilogarithm

  • Khodabakhsh Hessami Pilehrood
  • Tatiana Hessami Pilehrood
  • Wadim Zudilin
Article
  • 61 Downloads

Abstract

We prove that, for z ∈ {1/2, 2/3, 3/4, 4/5}, at least one of the two numbers Open image in new window is irrational.

Mathematics Subject Classification (2000)

11J72 11G55 33C20 33C60 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • Khodabakhsh Hessami Pilehrood
    • 1
    • 2
  • Tatiana Hessami Pilehrood
    • 1
    • 2
  • Wadim Zudilin
    • 3
  1. 1.School of MathematicsInstitute for Studies in Theoretical Physics and MathematicsTehranIran
  2. 2.Mathematics DepartmentShahrekord UniversityShahrekordIran
  3. 3.Department of Mechanics and MathematicsMoscow Lomonosov State UniversityMoscowRussia

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