Arithmetic of linear forms involving odd zeta values

Details Arithmetic of linear forms involving odd zeta values Arithmetic of linear forms involving odd zeta values

2002-06-18

arxiv.org/abs/math/0206176v2

J. Th\'eorie Nombres Bordeaux 16:1 (2004), 251--291

Mathematics

Number Theory

42 pages, LaTeX; slight modification of the absract

Scientific paper

A general hypergeometric construction of linear forms in (odd) zeta values is presented. The construction allows to recover the records of Rhin and Viola for the irrationality measures of $\zeta(2)$ and $\zeta(3)$, as well as to explain Rivoal's "infinitely-many" result (math.NT/0008051) and to prove that at least one of the four numbers $\zeta(5)$, $\zeta(7)$, $\zeta(9)$, and $\zeta(11)$ is irrational.

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