  We give a necessary and sufficient condition for the integrality of the
Taylor coefficients of mirror maps at the origin. By mirror maps, we mean
formal power series z.exp(G(z)/F(z)), where F(z) and G(z)+log(z)F(z) are
particular solutions of certain generalized hypergeometric differential
equations. This criterion is based on the analytical properties of Landau's
function (which is classically associated to the sequences of factorial ratios)
and it generalizes results proved by Krattenthaler-Rivoal in "On the
integrality of the Taylor coefficients of mirror maps" (to appear in Duke Math.
J.). One of the techniques used to prove this criterion is a generalization of
a theorem of Dwork on the formal congruences between formal series, which
proved to be insufficient for our purposes.
