Sur l'infimum des parties r\'eelles des z\'eros des sommes partielles de la fonction z\^eta de Riemann

Abstract

The greatest lower bound of the real parts of the roots of a partial sum of the Dirichlet series of Riemann's zeta function is asymptotically equivalent to the opposite of the number of terms of this sum, multiplied by the Napierian logarithm of 2, when this number of terms tends to infinity.