Abstract
We propose a new method for proving the Zudilin-Rivoal theorem stating, in particular, that the sequence of values of the Dirichlet beta function at even natural points contains infinitely many irrational values. For polylogarithms, we use Hermite—Padé approximations of the first type, invariant with respect to the Klein group. Quantitative additions to this theorem are obtained.
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Original Russian Text © V. N. Sorokin, 2007, published in Matematicheskie Zametki, 2007, Vol. 81, No. 6, pp. 912–923.
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Sorokin, V.N. On the Zudilin-Rivoal theorem. Math Notes 81, 817–826 (2007). https://doi.org/10.1134/S000143460705029X
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DOI: https://doi.org/10.1134/S000143460705029X