Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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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

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.
References
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Bibliographic Information
  • Josep Àlvarez Montaner
  • Affiliation: Departament de Matemàtiques and Institut de Matemàtiques de la UPC-Barcelona Tech (IMTech), Universitat Politècnica de Catalunya, Av. Diagonal 647, Barcelona 08028, Spain; and Centre de Recerca Matemàtica (CRM), Bellaterra, Barcelona 08193, Spain
  • ORCID: 0000-0001-6793-368X
  • Email: josep.alvarez@upc.edu
  • Manuel González Villa
  • Affiliation: Centro de investigación en Matemáticas, Apartado Postal 402, C.P. 36000, Guanajuato, GTO, México; and (temporarily) Departamento de Matemáticas, IUMA, Universidad de Zaragoza C. Pedro Cerbuna 12, 50009 Zaragoza, Spain
  • ORCID: 0000-0002-0370-3401
  • Email: manuel.gonzalez@cimat.mx, m.gonzalez@unizar.es
  • Edwin León-Cardenal
  • Affiliation: Departamento de Matemáticas y Computación, Universidad de La Rioja, C. Madre de Dios 53, 26006 Logroño, Spain; CONAHCYT–Centro de investigación en Matemáticas, Unidad Zacatecas, Av. Lasec Andador Galileo Galilei, Manzana 3 Lote 7, C.P. 98160, Zacatecas, ZAC, México
  • ORCID: 0000-0002-3171-0334
  • Email: edwin.leon@unirioja.es, edwin.leon@cimat.mx
  • Luis Núñez-Betancourt
  • Affiliation: Centro de investigación en Matemáticas, Apartado Postal 402, C.P. 36000, Guanajuato, GTO, México
  • MR Author ID: 949465
  • Email: luisnub@cimat.mx
  • Received by editor(s): December 23, 2022
  • Received by editor(s) in revised form: September 14, 2024, and December 22, 2024
  • Published electronically: January 30, 2025
  • Additional Notes: The first author was partially supported by the projects PID2019-103849GB-I00 and PID2023-146936NB-I00 financed by the Spanish State Agency MCIN/AEI/10.13039/501100011033/ FEDER, UE, by the GEOMVAP 2021-SGR-00603 AGAUR project and Spanish State Research Agency, through the Severo Ochoa and María de Maeztu Program for Centers and Units of Excellence in R$\&$D (project CEX2020-001084-M)
    The second author was partially supported by CONACyT Grant No. 320393, by MCIN/AEI/10.13039/501100011033 (codes PID2020-114750GB-C31 and PID2020-114750GB-C33), by Departamento de Ciencia, Universidad y Sociedad del Conocimiento del Gobierno de Aragón (grant code: E22_20R: “Álgebra y Geometría”), and by the European Union NextGenerationEU/PRTR and UNIZAR via María Zambrano’s Program.
    The third author was partially supported by MCIN/AEI/10.13039/501100011033 (grant code: PID2020-114750GB-C31) and by Departamento de Ciencia, Universidad y Sociedad del Conocimiento del Gobierno de Aragón (grant code: E22_20R: “Álgebra y Geometría”). Funded by the European Union NextGenerationEU/PRTR and UNIZAR via María Zambrano’s Program and also partially supported by CONAHCYT project CF-2023-G33.
    The fourth author was partially supported by CONAHCyT Grants 284598, CBF 2023-2024-224, CF-2023-G-33 and Cátedras Marcos Moshinsky.
  • Dedicated: In memory of Professor Roberto Callejas-Bedregal
  • © Copyright 2025 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 378 (2025), 4929-4954
  • MSC (2020): Primary 14F10; Secondary 46F10, 32S45, 14E15, 14F18, 13N10
  • DOI: https://doi.org/10.1090/tran/9390