Publicado

1997-07-01

Zeta functions of singular curves over finite fields

Palabras clave:

Zeta functions, finite fields, singular curves, generalized Jacobians, compactified Jacobians (es)

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Autores/as

  • Wilson Alvaro Zúñiga Galindo Universidad. Autónoma de Bucaramanga

 Let X be a complete, geometrically irreducible, algebraic curve defined over a finite field Fq and let ς (X,t) be its zeta function [Ser1], If X is a singular curve, two other zeta functions exist. The first is the Dirichlet series Z(Ca(X), t) associated to the effective Cartier divisors on X; the second is the Dirichlet series Z(Div(X),t) associated to the effective divisors on X, In this paper we generalize F. K. Schmidt's results on the rationality and functional equation of the zeta function ς(X, t) of a non-singular curve to the functions Z(Ca(X), t) and Z(Div(X), t) by means ofthe singular Riemann-Roch theorem.

Cómo citar

APA

Zúñiga Galindo, W. A. (1997). Zeta functions of singular curves over finite fields. Revista Colombiana de Matemáticas, 31(2), 115–124. https://revistas.unal.edu.co/index.php/recolma/article/view/33674

ACM

[1]
Zúñiga Galindo, W.A. 1997. Zeta functions of singular curves over finite fields. Revista Colombiana de Matemáticas. 31, 2 (jul. 1997), 115–124.

ACS

(1)
Zúñiga Galindo, W. A. Zeta functions of singular curves over finite fields. rev.colomb.mat 1997, 31, 115-124.

ABNT

ZÚÑIGA GALINDO, W. A. Zeta functions of singular curves over finite fields. Revista Colombiana de Matemáticas, [S. l.], v. 31, n. 2, p. 115–124, 1997. Disponível em: https://revistas.unal.edu.co/index.php/recolma/article/view/33674. Acesso em: 29 mar. 2024.

Chicago

Zúñiga Galindo, Wilson Alvaro. 1997. «Zeta functions of singular curves over finite fields». Revista Colombiana De Matemáticas 31 (2):115-24. https://revistas.unal.edu.co/index.php/recolma/article/view/33674.

Harvard

Zúñiga Galindo, W. A. (1997) «Zeta functions of singular curves over finite fields», Revista Colombiana de Matemáticas, 31(2), pp. 115–124. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/33674 (Accedido: 29 marzo 2024).

IEEE

[1]
W. A. Zúñiga Galindo, «Zeta functions of singular curves over finite fields», rev.colomb.mat, vol. 31, n.º 2, pp. 115–124, jul. 1997.

MLA

Zúñiga Galindo, W. A. «Zeta functions of singular curves over finite fields». Revista Colombiana de Matemáticas, vol. 31, n.º 2, julio de 1997, pp. 115-24, https://revistas.unal.edu.co/index.php/recolma/article/view/33674.

Turabian

Zúñiga Galindo, Wilson Alvaro. «Zeta functions of singular curves over finite fields». Revista Colombiana de Matemáticas 31, no. 2 (julio 1, 1997): 115–124. Accedido marzo 29, 2024. https://revistas.unal.edu.co/index.php/recolma/article/view/33674.

Vancouver

1.
Zúñiga Galindo WA. Zeta functions of singular curves over finite fields. rev.colomb.mat [Internet]. 1 de julio de 1997 [citado 29 de marzo de 2024];31(2):115-24. Disponible en: https://revistas.unal.edu.co/index.php/recolma/article/view/33674

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