Construction of Approximations to Zeta-Values

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


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.


Irrationality polylogarithms zeta-function 

2000 Mathematics subject classification



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© Springer-Verlag 2008

Authors and Affiliations

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

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