The Poincare series of multiplier ideals of a simple complete ideal in a local ring of a smooth surface

For a simple complete ideal p of a local ring at a closed point on a smooth complex algebraic surface, we introduce an algebraic object, named Poincare series P-p, that gathers in a unified way the jumping numbers and the dimensions of the vector space quotients given by consecutive multiplier ideals attached to p. This paper is devoted to prove that P-p is a rational function giving an explicit expression for it. (C) 2010 Elsevier Inc. All rights reserved.