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Many values of the Riemann zeta function at odd integers are irrational

Fischler, Stéphane ; Sprang, Johannes ; Zudilin, Wadim



Abstract

In this note, we announce the following result: at least 2((1-epsilon)log s/log log s) values of the Riemann zeta function at odd integers between 3 and s are irrational, where s is any positive real number and s is large enough in terms of epsilon. This improves on the lower bound 1-epsilon/1+log 2 log s that follows from the Ball-Rivoal theorem. We give the main ideas of the proof, which is ...

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