Counting Points of the Curve y⁴=x³+a over a Finite Field | Synapse
April 4, 2026Open Access
Counting Points of the Curve y⁴=x³+a over a Finite Field
Key Points
This research aims to derive formulas for counting rational points and evaluating the congruence zeta function of specific curves over finite fields.
Derived explicit formulas for the number of rational points on curves
Analyzed the congruence zeta functions for non-singular complete curves
Focused on curves defined by the equation y^4 = x^3 + a
Established explicit formulas for the rational points on the curve
Determined the form of the congruence zeta function for the given curve
Presented implications for the study of curves over finite fields
Abstract
We give explicit formulas of the number of rational points and of the congruence zeta function for a non-singular complete curve over a finite field defined by an affine equation y 4 = x 3 + a.