  A modified $A$-hypergeometric system is a system of differential equations
for the function $f(t^w \cdot x)$ where $f(y)$ is a solution of an
$A$-hypergeometric system in $n$ variables and $w$ is an $n$ dimensional
integer vector, which is called the weight vector. We study the irregularity of
modified systems by adapting to this case the notion of umbrella introduced by
M. Schulze and U. Walther. Especially, we study slopes and Gevrey series
solutions. We develop some applications of this study. Under some conditions we
give Laplace integral representations of divergent series solutions of the
modified system and we show that certain Gevrey series solutions of the
original $A$-hypergeometric system along coordinate varieties are Gevrey
asymptotic expansions of holomorphic solutions of the $A$-hypergeometric
system.
