Construction of Class Fields and Zeta Functions of Algebraic Curves

1967 ◽  
Vol 85 (1) ◽  
pp. 58 ◽  
Author(s):  
Goro Shimura
Keyword(s):  
Algebraic Curves ◽  
Zeta Functions ◽  
Class Fields

scholarly journals Motivic zeta functions for curve singularities

2010 ◽  
Vol 198 ◽  
pp. 47-75 ◽  
Author(s):  
J. J. Moyano-Fernández ◽  
W. A. Zúňiga-Galindo
Keyword(s):  
Functional Equation ◽  
Zeta Function ◽  
Local Ring ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Zeta Functions ◽  
Poincaré Series ◽  
Poincare Series ◽  
Motivic Zeta Functions ◽  
Curve Singularities

AbstractLet 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.

scholarly journals Motivic zeta functions for curve singularities

2010 ◽  
Vol 198 ◽  
pp. 47-75
Author(s):  
J. J. Moyano-Fernández ◽  
W. A. Zúňiga-Galindo
Keyword(s):  
Functional Equation ◽  
Zeta Function ◽  
Local Ring ◽  
Algebraic Curve ◽  
Algebraic Curves ◽  
Zeta Functions ◽  
Poincaré Series ◽  
Poincare Series ◽  
Motivic Zeta Functions ◽  
Curve Singularities

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.

scholarly journals Recovering algebraic curves from L-functions of Hilbert class fields

2020 ◽  
Vol 6 (4) ◽  
Author(s):  
Jeremy Booher ◽  
José Felipe Voloch
Keyword(s):  
Algebraic Curves ◽  
Class Fields
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