在某些形式为y3 = f(x)的fp2极大曲线上

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2025-06-20 DOI:10.1016/j.ffa.2025.102682

Guilherme Dias, Saeed Tafazolian

引用次数: 0

摘要

我们研究了有限域上与Chebyshev多项式φd(x)相关的代数曲线的极大性。具体地，我们研究了由v3=φd(u)给出的曲线C，并确定了这些曲线达到Hasse-Weil上界的所有有限域。我们的结果推广了先前关于超椭圆曲线的研究。此外，我们在整个论文中考察了y3=f(x)形式的其他相关曲线。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On certain Fp2-maximal curves of the form y3 = f(x)

We investigate the maximality of algebraic curves associated with Chebyshev polynomials

φ_{d} (x)

, over finite fields. Specifically, we study the curve

C

given by

v^{3} = φ_{d} (u)

and determine all finite fields over which these curves attain the Hasse–Weil upper bound. Our results generalize previous work that focused on hyperelliptic curves. Additionally, we examine other related curves of the form

y^{3} = f (x)

throughout the paper.

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来源期刊

Finite Fields and Their Applications 数学-数学

CiteScore

2.00

自引率

20.00%

发文量

133

审稿时长

6-12 weeks

期刊介绍： Finite Fields and Their Applications is a peer-reviewed technical journal publishing papers in finite field theory as well as in applications of finite fields. As a result of applications in a wide variety of areas, finite fields are increasingly important in several areas of mathematics, including linear and abstract algebra, number theory and algebraic geometry, as well as in computer science, statistics, information theory, and engineering. For cohesion, and because so many applications rely on various theoretical properties of finite fields, it is essential that there be a core of high-quality papers on theoretical aspects. In addition, since much of the vitality of the area comes from computational problems, the journal publishes papers on computational aspects of finite fields as well as on algorithms and complexity of finite field-related methods. The journal also publishes papers in various applications including, but not limited to, algebraic coding theory, cryptology, combinatorial design theory, pseudorandom number generation, and linear recurring sequences. There are other areas of application to be included, but the important point is that finite fields play a nontrivial role in the theory, application, or algorithm.

在某些形式为y3 = f(x)的fp2极大曲线上

摘要

在某些形式为y3 = f(x)的fp2极大曲线上