Zeta Functions of Curves over Finite Fields with Many Rational Points

2000 ◽  
pp. 167-174 ◽  
Author(s):  
Kristin Lauter
Keyword(s):  
Finite Fields ◽  
Zeta Functions ◽  
Rational Points ◽  
Curves Over Finite Fields

Rational points and zeta functions of some curves over finite fields

2010 ◽  
Vol 53 (11) ◽  
pp. 2855-2863
Author(s):  
Long Wang ◽  
JinQuan Luo
Keyword(s):  
Finite Fields ◽  
Zeta Functions ◽  
Rational Points ◽  
Curves Over Finite Fields

Rational points on Fermat curves over finite fields

2017 ◽  
Vol 16 (03) ◽  
pp. 1750046
Author(s):  
Wei Cao ◽  
Shanmeng Han ◽  
Ruyun Wang
Keyword(s):  
Finite Fields ◽  
Rational Point ◽  
Rational Points ◽  
Fermat Curve ◽  
Fermat Curves ◽  
Curves Over Finite Fields

Let [Formula: see text] be the [Formula: see text]-rational point on the Fermat curve [Formula: see text] with [Formula: see text]. It has recently been proved that if [Formula: see text] then each [Formula: see text] is a cube in [Formula: see text]. It is natural to wonder whether there is a generalization to [Formula: see text]. In this paper, we show that the result cannot be extended to [Formula: see text] in general and conjecture that each [Formula: see text] is a cube in [Formula: see text] if and only if [Formula: see text].

A Note on Relations Between the Zeta-Functions of Galois Coverings of Curves Over Finite Fields

1990 ◽  
Vol 33 (3) ◽  
pp. 282-285 ◽  
Author(s):  
Amilcar Pacheco
Keyword(s):  
Finite Field ◽  
Finite Fields ◽  
Group Ring ◽  
Algebraic Curve ◽  
Zeta Functions ◽  
Finite Subgroup ◽  
Rational Group ◽  
Galois Coverings ◽  
Curves Over Finite Fields ◽  
Special Case

AbstractLet C be a complete irreducible nonsingular algebraic curve defined over a finite field k. Let G be a finite subgroup of the group of automorphisms Aut(C) of C. We prove that certain idempotent relations in the rational group ring Q[G] imply other relations between the zeta-functions of the quotient curves C/H, where H is a subgroup of G. In particular we generalize some results of Kani in the special case of curves over finite fields.

On the number of rational points of curves over finite fields

2013 ◽  
Vol 40 ◽  
pp. 21-26
Author(s):  
Nurdagül Anbar ◽  
Henning Stichtenoth
Keyword(s):  
Finite Fields ◽  
Rational Points ◽  
Curves Over Finite Fields
Sign in / Sign up

Export Citation Format

Share Document