What question did this study set out to answer?

This research aims to derive formulas for counting rational points and evaluating the congruence zeta function of specific curves over finite fields.

April 4, 2026Open Access

Counting Points of the Curve y⁴=x³+a over a Finite Field

Puntos clave

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

Resumen

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.

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Cite This Study

Ozaki Eiji (Fri,) studied this question.

synapsesocial.com/papers/69d0adc2659487ece0fa43e3 https://doi.org/https://doi.org/10.14992/00008665