Igusa’s local zeta functions of semiquasihomogeneous polynomials

Zúñiga-Galindo, W.

doi:10.1090/S0002-9947-01-02323-6

Igusa’s local zeta functions of semiquasihomogeneous polynomials
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by W. A. Zúñiga-Galindo

Trans. Amer. Math. Soc. 353 (2001), 3193-3207

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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