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Rational points on cubic, quartic and sextic curves over finite fields
Journal of Number Theory ( IF 0.6 ) Pub Date : 2021-02-23 , DOI: 10.1016/j.jnt.2021.01.018
José Alves Oliveira

Let Fq denote the finite field with q elements. In this work, we use characters to give the number of rational points on suitable curves of low degree over Fq in terms of the number of rational points on elliptic curves. In the case where q is a prime number, we give a way to calculate these numbers. As a consequence of these results, we characterize maximal and minimal curves given by equations of the forms ax3+by3+cz3=0 and ax4+by4+cz4=0.



中文翻译:

有限域上三次,四次和六边形曲线上的有理点

Fq表示带有q个元素的有限域。在这项工作中,我们使用字符来给出适当的低度曲线上有理点的数量。Fq椭圆曲线上有理点的数量 在q是素数的情况下,我们提供了一种计算这些数字的方法。这些结果的结果是,我们表征了形式方程式给出的最大和最小曲线一种X3+bÿ3+Cž3=0一种X4+bÿ4+Cž4=0

更新日期:2021-02-26
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