Organisateurs: Michel Balazard (CNRS, Laboratoire Poncelet) , Michael Tsfasman (CNRS, Laboratoire Poncelet, Institut des Probl mes de Transmission de l'Information) , Alexey Zykin (Laboratoire Poncelet, Haute Ecole d'Economie) . ... In that talk, I will explain how some considerations concerning the Nyman criterion for the Riemann hypothesis led us to investigate the local behaviour of the Brjuno function $\Phi$ initially introduced to study some complex dynamical systems. ... Laboratoire Poncelet . ...