Bernstein-Sato polynomial and related invariants for meromorphic functions
Complex Variables
2025-05-19 v2 Commutative Algebra
Algebraic Geometry
Abstract
We develop a theory of Bernstein-Sato polynomials for meromorphic functions and we use it to study the analytic continuation of Archimedian local zeta functions in this setting. We also introduce both an analytic and an algebraic theory of multiplier ideals for meromorphic functions and relate the jumping numbers of these multiplier ideals to the roots of the Bernstein-Sato polynomials.
Keywords
Cite
@article{arxiv.2112.08492,
title = {Bernstein-Sato polynomial and related invariants for meromorphic functions},
author = {Josep Àlvarez Montaner and Manuel González Villa and Edwin León-Cardenal and Luis Núñez-Betancourt},
journal= {arXiv preprint arXiv:2112.08492},
year = {2025}
}
Comments
25 pages. Major changes in Sections 2 and 3 due to an error in a previous version. Comments welcome