Arithmetic of linear forms involving odd zeta values
Wadim Zudilin
Abstract
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 ζ(2) and ζ(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 ζ(5), ζ(7), ζ(9), and ζ(11) is irrational.
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