Arithmetic of linear forms involving odd zeta values

By Wadim Zudilin. 2002

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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:

Subfields: Algebra and Number Theory, Applied Mathematics

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