The Intersection Structure of Bernstein-Sato Ideals

By using logarithmic $\mathcal{D}$-modules and Gröbner bases, we prove that Bernstein-Sato ideals satisfy some symmetric intersection property, answering a question posed by Budur. As an application, we obtain a formula for the Bernstein-Sato polynomials of $f^n$, the integer powers of a multi-variable polynomial $f$.