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Wadim Zudilin
Well-poised hypergeometric service for diophantine problems of zeta values
Journal de théorie des nombres de Bordeaux, 15 no. 2 (2003), p. 593-626, doi: 10.5802/jtnb.415
Article PDF | Reviews MR 2140869 | Zbl 02184613 | 2 citations in Cedram

Résumé - Abstract

It is explained how the classical concept of well-poised hypergeometric series and integrals becomes crucial in studying arithmetic properties of the values of Riemann’s zeta function. By these well-poised means we obtain: (1) a permutation group for linear forms in $1$ and $\zeta (4) = \pi ^4/90$ yielding a conditional upper bound for the irrationality measure of $\zeta (4)$; (2) a second-order Apéry-like recursion for $\zeta (4)$ and some low-order recursions for linear forms in odd zeta values; (3) a rich permutation group for a family of certain Euler-type multiple integrals that generalize so-called Beukers’ integrals for $\zeta (2)$ and $\zeta (3)$.

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