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