Abstract
To any $f \in \C[x_{1}, \ldots, x_{n}] \setminus \C$ with $f(0) = 0$ one can associate the motivic zeta function. Another interesting singularity invariant of $f^{-1}\!\{0\}$ is the zeta function on the level of Hodge polynomials, which is actually just a specialization of the motivic one. In this paper we generalize for the Hodge zeta function the result of Veys which provided for $n = 2$ a complete geometric determination of the poles. More precisely we give in arbitrary dimension a complete geometric determination of the poles of order $n-1$ and $n$. We also show how to obtain the same results for the motivic zeta function.
Citation
B. Rodrigues. "Geometric determination of the poles of highest and second highest order of Hodge and motivic zeta functions." Nagoya Math. J. 176 1 - 18, 2004.
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