  We study multiplicities of jumping numbers of multiplier ideals in a smooth
variety of arbitrary dimension. We prove that the multiplicity function is a
quasi-polynomial, hence proving that the Poincar\'e series is a rational
function. We further study when the various components of the quasi-polynomial
have the highest possible degree and relate it to jumping numbers contributed
by Rees valuations. Finally, we study the special case of monomial ideals.
