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Poincare series and zeta function for an irreducible plane curve singularity

Jan Stevens
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Abstract

The Poincare series of an irreducible plane curve singularity equals the zeta function of its monodromy, by a result of Campillo, Delgado and Gusein-Zade. We derive this fact from a formula of Ebeling and Gusein-Zade relating the Poincare series of a quasi-homogeneous complete intersection singularity to the Saito dual of a product of zeta functions.

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Jan Stevens. 2003-10-15. Poincare series and zeta function for an irreducible plane curve singularity. https://arxiv.org/abs/math/0310215

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