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

摘要

In this note, we announce the following result: at least2(1?ε)log?slog?log?svalues of the Riemann zeta function at odd integers between 3 andsare irrational, whereεis any positive real number andsis large enough in terms ofε. This improves on the lower bound1?ε1+log?2log?sthat 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.