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Matematicheskie Zametki, 2007, Volume 81, Issue 6, Pages 912–923
DOI: https://doi.org/10.4213/mzm3742 (Mi mzm3742) 		 
This article is cited in 4 scientific papers (total in 4 papers)

On the Zudilin–Rivoal Theorem

V. N. Sorokin

M. V. Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
Full-text PDF (447 kB) Citations (4)
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DOI: https://doi.org/10.4213/mzm3742
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.
Received: 27.12.2004
English version:
Mathematical Notes, 2007, Volume 81, Issue 6, Pages 817–826
DOI: https://doi.org/10.1134/S000143460705029X
Bibliographic databases:
UDC: 511.3
Language: Russian
Citation: V. N. Sorokin, “On the Zudilin–Rivoal Theorem”, Mat. Zametki, 81:6 (2007), 912–923; Math. Notes, 81:6 (2007), 817–826
Citation in format AMSBIB
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    • This publication is cited in the following 4 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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