Bernstein-Sato polynomial and related invariants for meromorphic functions

Àlvarez Montaner, Josep; González Villa, Manuel; León-Cardenal, Edwin; Núñez-Betancourt, Luis

doi:10.1090/tran/9390

Bernstein-Sato polynomial and related invariants for meromorphic functions
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by Josep Àlvarez Montaner, Manuel González Villa, Edwin León-Cardenal and Luis Núñez-Betancourt;

Trans. Amer. Math. Soc. 378 (2025), 4929-4954

DOI: https://doi.org/10.1090/tran/9390

Published electronically: January 30, 2025

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Abstract:

We develop a theory of Bernstein-Sato polynomials for meromorphic functions. As a first application we study the poles of Archimedian local zeta functions for meromorphic germs. We also present a theory of multiplier ideals for meromorphic functions from the analytic and algebraic point of view. It is also shown that the jumping numbers of these multiplier ideals are related with the roots of the Bernstein-Sato polynomials.

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Bernstein-Sato polynomial and related invariants for meromorphic functions
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Abstract: