  We prove that certain roots of the Bernstein-Sato polynomial (i.e.
b-function) are jumping coefficients up to a sign, showing a partial converse
of a theorem of L. Ein, R. Lazarsfeld, K.E. Smith, and D. Varolin. We also
prove that certain roots are determined by a filtration on the Milnor
cohomology, generalizing a theorem of B. Malgrange in the isolated singularity
case. This implies a certain relation with the spectrum which is determined by
the Hodge filtration, because the above filtration is related to the pole order
filtration. For multiplier ideals we prove an explicit formula in the case of
locally conical divisors along a stratification, generalizing a formula of
Mustata in the case of hyperplane arrangements. We also give another proof of a
formula of U. Walther on the b-function of a generic hyperplane arrangement,
including the multiplicity of -1.
