Resumo: Let O = C{X} := C{X1,..., Xn} be the ring of germs of holomorphic functions at the origin of Cn and D_X[s] the ring of differential operators over O and polynomial in s. The Bernstein-Sato polynomial bf(s) of f(X) ∈ O is the monic polynomial b(s) ∈ C[s] of the least degree that satisfies P(X, s, ∂/∂X )f (X)^{s+1} = b(s)f (X)^s, with some P(X, s, ∂/∂X ) ∈ D_X [s]. For f ∈ O with isolated singularity at the origin, some sets of invariants have been related to the roots of bf(s), among them we have the set of spectral numbers whose relation with roots of bf(s) has been studied by many authors.
In this talk we will present a relation between the roots of bf(s), the spectral numbers and the set of values of differentials on an irreducible plane curve given by f = 0.