Nagoya Mathematical Journal

Motivic zeta functions for curve singularities

J. J. Moyano-Fernández and W. A. Zúñiga-Galindo

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Let X be a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristic p big enough. Given a local ring OP,X at a rational singular point P of X, we attached a universal zeta function which is a rational function and admits a functional equation if OP,X is Gorenstein. This universal zeta function specializes to other known zeta functions and Poincaré series attached to singular points of algebraic curves. In particular, for the local ring attached to a complex analytic function in two variables, our universal zeta function specializes to the generalized Poincaré series introduced by Campillo, Delgado, and Gusein-Zade.

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Nagoya Math. J., Volume 198 (2010), 47-75.

First available in Project Euclid: 10 May 2010

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Zentralblatt MATH identifier

Primary: 14H20: Singularities, local rings [See also 13Hxx, 14B05] 14G10: Zeta-functions and related questions [See also 11G40] (Birch- Swinnerton-Dyer conjecture)
Secondary: 32S40: Monodromy; relations with differential equations and D-modules 11S40: Zeta functions and $L$-functions [See also 11M41, 19F27]


Moyano-Fernández, J. J.; Zúñiga-Galindo, W. A. Motivic zeta functions for curve singularities. Nagoya Math. J. 198 (2010), 47--75. doi:10.1215/00277630-2009-007.

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