The Poles of Igusa Zeta Integrals and the Unextendability of Semi-invariant Distributions

Abstract

Abstract 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.