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Construction of Approximations to Zeta-Values

  • Yuri V. Nesterenko
Conference paper
Part of the Developments in Mathematics book series (DEVM, volume 16)

Abstract

Polylogarithmic functions are defined by series
$$ L_k \left( z \right) = \sum\limits_{v = 1}^\infty {\frac{{z^v }} {{v^k }}} , k \geqslant 1. $$
Due to equalities Lk;(1) = ζ(k), k ≥ 2, they play an important role in study of arithmetic properties of Riemann zeta-function ζ(s) at integer points.

Keywords

Irrationality polylogarithms zeta-function 

2000 Mathematics subject classification

11J72 

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Copyright information

© Springer-Verlag 2008

Authors and Affiliations

  • Yuri V. Nesterenko
    • 1
  1. 1.Faculty of Mechanics and MathematicsMoscow Lomonosov State UniversityMoscowRussia

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