Poincare series and zeta function for an irreducible plane curve singularity

2003/10/15 by Jan Stevens, Stevens, Jan
Mathematics · #Algebraic Geometry and Number Theory #Analytic Number Theory Research #Meromorphic and Entire Functions #math.AG #msc:14B05 #msc:32S40

paper · pdf · doi:10.48550/arxiv.math/0310215

7 pages

arxiv created 2003/10/15 · arxiv updated 2009/12/01

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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