Motivic zeta functions for curve singularities
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AbstractLetXbe a complete, geometrically irreducible, singular, algebraic curve defined over a field of characteristicpbig enough. Given a local ringOp,x at a rational singular pointPofX, we attached a universal zeta function which is a rational function and admits a functional equation ifOp,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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2008 ◽
Vol 262
(4)
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pp. 849-866
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1980 ◽
Vol 32
(5)
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pp. 1261-1265
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2019 ◽
Vol 295
(1-2)
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pp. 427-462
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2012 ◽
Vol 48
(3)
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pp. 653-660
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2008 ◽
Vol 137
(01)
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pp. 51-59
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