4 research outputs found
On the Zeta Functions of Supersingular Curves
In general, the L-polynomial of a curve of genus is determined by
coefficients. We show that the L-polynomial of a supersingular curve of genus
is determined by fewer than coefficients
Divisibility of L-Polynomials for a Family of Artin-Schreier Curves
In this paper we consider the curves
defined over and give a positive answer to a conjecture about a
divisibility condition on -polynomials of the curves . Our
proof involves finding an exact formula for the number of -rational points on for all , and uses a result we
proved elsewhere about the number of rational points on supersingular curves
Number of Rational points of the Generalized Hermitian Curves over
In this paper we consider the curves
over and and find an exact formula for the number of -rational points on for all integers . We also
give the condition when the -polynomial of a Hermitian curve divides the
-polynomial of another over
On the Zeta function and the automorphism group of the generalized Suzuki curve
For an odd prime number, , and , let
be the nonsingular model of In the present work, the number of
-rational points and the full automorphism group of
are determined. In addition, the
L-polynomial of this curve is provided, and the number of
-rational points on the Jacobian
is used to construct \'{e}tale
covers of , some with many rational
points