Padé approximants and balanced hypergeometric series.

DOI10.1016/S0021-7824(03)00027-8zbMath1064.11053MaRDI QIDQ1415341

Tanguy Rivoal, Stéphane Fischler

Publication date: 3 December 2003

Published in: Journal de Mathématiques Pures et Appliquées. Neuvième Série (Search for Journal in Brave)

zbMATH Keywords

Riemann zeta functionhypergeometric seriesPadé approximantsDiophantine approximation

Mathematics Subject Classification ID

Transcendence theory of other special functions (11J91) Irrationality; linear independence over a field (11J72)

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Euler numbers, Padé approximants and Catalan's constant ⋮ Irrationality of certain numbers that contain values of the di- and trilogarithm ⋮ Unnamed Item ⋮ Irrationality of the sums of zeta values ⋮ Simultaneous Padé approximants to the Euler, exponential and logarithmic functions ⋮ A lower bound of the dimension of the vector space spanned by the special values of certain functions ⋮ Approximants de Padé des q-Polylogarithmes ⋮ Hypergeometric series and irrationality of the values of the Riemann zeta function ⋮ Séries hypergéométriques multiples et polyzêtas ⋮ Irrationality of values of L‐functions of Dirichlet characters ⋮ Distribution of irrational zeta values ⋮ The Hurwitz zeta function as a convergent series ⋮ Linear independence of values of \(G\)-functions. II: Outside the disk of convergence ⋮ SHIDLOVSKY’S MULTIPLICITY ESTIMATE AND IRRATIONALITY OF ZETA VALUES

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