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Transactions of the American Mathematical Society

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Igusa's local zeta functions of semiquasihomogeneous polynomials


Author: W. A. Zúñiga-Galindo
Journal: Trans. Amer. Math. Soc. 353 (2001), 3193-3207
MSC (2000): Primary 11D79, 11S40, 14G10
DOI: https://doi.org/10.1090/S0002-9947-01-02323-6
Published electronically: April 11, 2001
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Abstract:

In this paper, we prove the rationality of Igusa's local zeta functions of semiquasihomogeneous polynomials with coefficients in a non-archimedean local field $K$. The proof of this result is based on Igusa's stationary phase formula and some ideas on Néron $\pi $-desingularization.


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Additional Information

W. A. Zúñiga-Galindo
Affiliation: Universidad Autónoma de Bucaramanga, Laboratorio de Computo Especializado, A.A. 1642, Bucaramanga, Colombia
Address at time of publication: 6351 SW 43rd Street, Miami, Florida 33155
Email: wzuniga@bumanga.unab.edu.co

DOI: https://doi.org/10.1090/S0002-9947-01-02323-6
Keywords: Local zeta functions, semiquasihomogeneous polynomials, positive characteristic
Received by editor(s): June 3, 1997
Received by editor(s) in revised form: May 16, 2000
Published electronically: April 11, 2001
Additional Notes: This work was supported by COLCIENCIAS, contract #063-98
Article copyright: © Copyright 2001 American Mathematical Society