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New Irrationality Results for Dilogarithms of Rational Numbers

  • Carlo Viola
Part of the Developments in Mathematics book series (DEVM, volume 16)

Abstract

A natural method to investigate diophantine properties of transcendental (or conjecturally transcendental) constants occurring in various mathematical contexts consists in the search for sequences of good rational approximations, or algebraic approximations with bounded degree, to suitable values of some special transcendental functions, such as the logarithm, or the polylogarithm of order q ≤ 2, or the hypergeometric functions, etc. Traditionally, one employs for this purpose Padé or Padé-type approximations to the functions involved.

Keywords

Dilogarithm hypergeometric function permutation groups irrationality measures 

2000 Mathematics subject classification

11J82 33B30 33C05 20B35 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Carlo Viola
    • 1
  1. 1.Dipartimento di MatematicaUniversità di PisaPisaItaly

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