Well-poised hypergeometric service for diophantine problems of zeta values

Title: Well-poised hypergeometric service for diophantine problems of zeta values
Creator: Zudilin, W.
Relation: Journal de Théorie des Nombres de Bordeaux Vol. 15
Publisher Link: http://dx.doi.org/10.5802/jtnb.415
Publisher: Université de Bordeaux I
Resource Type: journal article
Date: 2003
Description: 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 ζ(4)=π 4 /90 yielding a conditional upper bound for the irrationality measure of ζ(4); (2) a second-order Apéry-like recursion for ζ(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 ζ(2) and ζ(3).
Subject: zeta function; integrals; irrationality
Identifier: http://hdl.handle.net/1959.13/935009
Identifier: uon:11942
Identifier: ISSN:1246-7405
Language: eng
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