Indicial polynomials and -functions of -modules along arbitrary varieties and their computation
arXiv:2605.27797
Abstract
We define an indicial polynomial of a -module along an arbitrary subvariety as a generalization of both the classical indicial polynomial for a single linear differential equation and the Bernstein-Sato polynomial of a variety defined by Budur-Mustata-Saito. An indicial polynomial is also a generalization of the -function of a -module along a submanifold and can be used in the computation of the -module theoretic inverse image by the embedding instead of the -function. We consider properties of indicial polynomials and relations with -functions. An indicial polynomial may exist even if the -function does not, and gives the set of the roots of the -function if it exists. Computation of an indicial polynomial is easier than the -function and naturally includes the case with parameters.
34 pages