This article is cited in 4 papers

On the Zudilin–Rivoal Theorem

V. N. Sorokin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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.

Keywords: Dirichlet beta function, Riemann zeta function, Hermite–Padé approximation, Zudilin–Rivoal theorem, polylogarithm, Klein group, Mellin transform.

UDC: 511.3

Received: 27.12.2004

DOI: 10.4213/mzm3742

 English version: Mathematical Notes, 2007, 81:6, 817–826

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