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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the relation between the generalized Poincaré series and the Stöhr zeta function


Authors: Félix Delgado de la Mata and Julio José Moyano Fernández
Journal: Proc. Amer. Math. Soc. 137 (2009), 51-59
MSC (2000): Primary 11M38; Secondary 14H20, 28A25
Published electronically: August 7, 2008
MathSciNet review: 2439424
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Abstract: The aim of this paper is to show the relation between the zeta function introduced by Stöhr and the Poincaré series of a curve singularity introduced by Campillo, Delgado and Gusein-Zade for the complex case. The interpretation of the Stöhr 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.


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Additional Information

Félix Delgado de la Mata
Affiliation: Departamento de Álgebra, Geometría y Topología, Facultad de Ciencias, Universidad de Valladolid, Valladolid, Spain
Email: fdelgado@agt.uva.es

Julio José Moyano Fernández
Affiliation: Institut für Mathematik, Universität Osnabrück, Albrechtstrasse 28a, 49069- Osnabrück, Germany
Email: moyano@agt.uva.es

DOI: http://dx.doi.org/10.1090/S0002-9939-08-09469-0
PII: S 0002-9939(08)09469-0
Keywords: Zeta function, Poincar\'e series, integration with respect to Euler characteristic, finite field
Received by editor(s): May 30, 2006
Received by editor(s) in revised form: May 18, 2007, and December 27, 2007
Published electronically: August 7, 2008
Additional Notes: The authors were partially supported by MEC MTM2004-00958 and by Junta de CyL VA068/04 (Spain). The second author was also supported by FPU-AP2003-2755.
Communicated by: Ted Chinburg
Article copyright: © Copyright 2008 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.