doi:10.1090/tran/9390engÀlvarez Montaner, JosepGonzález Villa, ManuelLeón-Cardenal, EdwinNúñez-Betancourt, LuisBernstein-Sato polynomial and related invariants for meromorphic functionsART-2025-143984We 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.2025http://zaguan.unizar.es/record/16524310.1090/tran/9390http://zaguan.unizar.es/record/165243oai:zaguan.unizar.es:165243info:eu-repo/grantAgreement/ES/DGA/E22-20Rinfo:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C31/AEI/10.13039/501100011033info:eu-repo/grantAgreement/ES/MICINN/PID2020-114750GB-C33/AEI/10.13039/501100011033TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY 378 (2025), 4929-4954by-nc-ndhttps://creativecommons.org/licenses/by-nc-nd/4.0/deed.esinfo:eu-repo/semantics/openAccess