Irrationality of values of zeta-function

We present several results on the number of irrational and linear independent values among $ζ(s),ζ(s+2),...,ζ(s+2n)$, where $s>2$ is an odd integer and $n>0$ is an integer. The main tool in our proofs is a certain generalization of Rivoal's construction (math.NT/0008051, math.NT/0104221).

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