2002/06/21 by Wadim Zudilin · 1 citation
Mathematics · #math.NT #math.CA #msc:11J72 #msc:11J82 #msc:33C60
published as J. Théorie Nombres Bordeaux 16:1 (2004), 251--291 · 42 pages, LaTeX; slight modification of the absract
arxiv created 2002/06/21 · arxiv updated 2009/11/30
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.