  We investigate the relationship between the poles of Igusa zeta integrals and
the unextendability of semi-invariant distributions. Under some algebraic
conditions, we obtain an upper bound for the order of the poles of Igusa zeta
integral, and by using the order of the poles we give a criterion on the
unextendability of semi-invariant distributions. A key ingredient of our method
is the idea of generalized semi-invariant distributions.
