On the b-function with respect to weights of annihilating ideals in the Weyl algebra

Given a polynomial $f\in\mathbb{C}[x_1,\ldots,x_n]$ and an integer $\ell\in\mathbb{Z}$, we study some properties of the b-function with respect to weights of the annihilating ideal Ann$(f^\ell)$. In some particular cases the expression of the b-function is given explicitly.

💡 Research Summary

The paper investigates the weighted b‑function associated with the annihilating ideal $\operatorname{Ann}(f^\ell)$ in the Weyl algebra $D_n=\mathbb{C}