  In this paper, we continue some work devoted to explicit zero-free discs for
a large class of Dirichlet series. In a previous article, such zero-free
regions were described using some spaces of functions which were defined with
some technical conditions. Here we give two different natural ways in order to
remove those technical conditions. In particular this allows to right down
explicit zero-free regions differently and to obtain for them an easier
description useful for direct applications.
