Upper Bounds for Roots of $b$-Functions, following Kashiwara and Lichtin

Abstract

By building on a method introduced by Kashiwara and refined by Lichtin, we give upper bounds for the roots of certain b-functions associated to a regular function f in terms of a log resolution of singularities. As applications, we recover with more elementary methods a result of Budur and Saito describing the multiplier ideals of f in terms of the V-filtration of f and a result of the second named author with Popa giving a lower bound for the minimal exponent of f in terms of a log resolution.