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 ...
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 based on an elimination process between several linear forms in odd zeta values with related coefficients. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS.
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