BERNSTEIN-SATO POLYNOMIALS FOR GENERAL IDEALS VS. PRINCIPAL IDEALS

We show that given an ideal a generated by regular functions f(1), ..., f(r) on X, the Bernstein-Sato polynomial of a is equal to the reduced Bernstein-Sato polynomial of the function g = Sigma(r)(i=1) f(i)y(i) on X x A(r). By combining this with results from Budur, Mustata, and Saito [Compos. Math. 142 (2006), pp. 779-797], we relate invariants and properties of a to those of g. We also use the result on Bernstein-Sato polynomials to show that the Strong Monodromy Conjecture for Igusa zeta functions of principal ideals implies a similar statement for arbitrary ideals.