Arithmetic of linear forms involving odd zeta values

  title={Arithmetic of linear forms involving odd zeta values},
  author={W. Zudilin},
  journal={Journal de Theorie des Nombres de Bordeaux},
  • W. Zudilin
  • Published 2002
  • Mathematics
  • Journal de Theorie des Nombres de Bordeaux
The story exposed in this paper starts in 1978, when R. Apery [Ap] gave a surprising sequence of exercises demonstrating the irrationality of ζ(2) and ζ(3). (For a nice explanation of Apery’s discovery we refer to the review [Po].) Although the irrationality of the even zeta values ζ(2), ζ(4), . . . for that moment was a classical result (due to L. Euler and F. Lindemann), Apery’s proof allows one to obtain a quantitative version of his result, that is, to evaluate irrationality exponents: 
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Keywords. Irrationality; Linear independence over a field; Measures of irrationality and of transcendence; Distribution modulo one.
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