Geodesic
On the Zudilin--Rivoal Theorem
Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 912-923

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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, Mellin transform.
Mots-clés : polylogarithm, Klein group 
@article{MZM_2007_81_6_a9,
     author = {V. N. Sorokin},
     title = {On the {Zudilin--Rivoal} {Theorem}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {912--923},
     publisher = {mathdoc},
     volume = {81},
     number = {6},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a9/}
}
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V. N. Sorokin. On the Zudilin--Rivoal Theorem. Matematičeskie zametki, Tome 81 (2007) no. 6, pp. 912-923. http://geodesic.mathdoc.fr/item/MZM_2007_81_6_a9/