Poincar\'e series of multiplier ideals in two-dimensional local rings   with rational singularities
  We study the multiplicity of the jumping numbers of an $\mathfrak m$-primary ideal $\mathfrak a$ in a two-dimensional local ring with a rational singularity. The formula we provide for the multiplicities leads to a very simple and efficient method to detect whether a given rational number is a jumping number. We also give an explicit description of the Poincar\'e series of multiplier ideals associated to $\mathfrak a$ proving, in particular, that it is a rational function. 
Maria Alberich-Carrami\~nana, Josep Alvarez Montaner, Ferran   Dachs-Cadefau, V\'ictor Gonz\'alez-Alonso
math.AG math.AC