Displaying similar documents to “On some iterated means arising in homogenization theory”

Arithmetic of linear forms involving odd zeta values

Wadim Zudilin (2004)

Journal de Théorie des Nombres de Bordeaux

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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 recent result on infiniteness of irrational numbers in the set of odd zeta values, and to prove that at least one of the four numbers ζ ( 5 ) , ζ ( 7 ) , ζ ( 9 ) , and ζ ( 11 ) is irrational.