On the relation between the generalized Poincare series and the Stohr zeta function

Autor(en): Delgado de la Mata, Felix
Moyano Fernandez, Julio Jose
Stichwörter: finite field; integration with respect to Euler characteristic; Mathematics; Mathematics, Applied; PLANE CURVE SINGULARITY; Poincare series; zeta function
Erscheinungsdatum: 2009
Herausgeber: AMER MATHEMATICAL SOC
Journal: PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY
Volumen: 137
Ausgabe: 1
Startseite: 51
Seitenende: 59
Zusammenfassung: 
The aim of this paper is to show the relation between the zeta function introduced by Stohr and the Poincare series of a curve singularity introduced by Campillo, Delgado and Gusein-Zade for the complex case. The interpretation of the Stohr zeta function in terms of integrals with respect to the (generalized) Euler characteristic over suitable subsets of the ring of functions (following the similar construction made by the previously named authors for subsets of the projectivization of the ring) provides the bridge between both subjects.
ISSN: 00029939

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