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In this work we studv some roots of the Bernstein polynomial bf associated to a germ f(X) in the maximal ideal of C j X i , . . . . A',,} with an isolated criticai point at the origin. It is known that for eacli root of bf tliere exists a spectral number such that the sum of these two nurnbcr.i is an mtcger. In general, one docsn't. kiiow how to compute explicitly these integers, although there are bonnds on tlieni. M. Sai to, in [Sa.i93], cxhibits a subset of the set of roots of bf, such i liai. for these eleinenis the sum is -1. Ileriling and Stahlke, in [HS99], succeeded to increase l.liis subset of roots, assuming / ( X ) in t\v variables, with isolated criticai point and finito monodrorny (such hypotheses are very rest: ;<tive). We succeeded to extend this last resuli without any restriction on the number of va:iables of f(X) and only with the as.auaptiou of isolated criticai point. Moreover, in the case of irreducible germs f ( X i , X 2 ) with only one Puiseux ])air, we show how to descriUa. larger subset of roots of bf, when / belongs te; a, given e(juidifereutiability class.

Polinômio de Bernstein-Sato de uma hipersuperfície com singularidade isolada