Regularity and b-functions for D-modules

Abstract

A holonomic D-module on a complex analytic manifoldadmits always a b-function along any submanifold. If the module is regular, itadmits also a regular b-function, that is a b-function with a condition on the order of the lower terms of the equation.There is a weaker condition of regularity: regularity alonga submanifold. We prove that a module which is regular alonga submanifold admits a regular b-function along this submanifold.