论二属超特殊曲线的罗森海恩形式

IF 1.2 3区 数学 Q1 MATHEMATICS
Ryo Ohashi
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引用次数: 0

摘要

本文研究了奇特征 p 中的超特殊属 2 曲线 C:y2=x(x-1)(x-λ)(x-μ)(x-ν)。作为主要结果,我们证明了{0,1,λ,μ,ν}中任意两个元素之差都是 Fp2 中的平方。此外,我们还证明了 C 在 Fp2 上是最大的或最小的,而无需考虑它的 Fp2 形式(我们给出了一个明确的 p 准则,告诉我们 C 是最大的还是最小的)。作为应用,我们还研究了属 3 和属 4 的超特殊超椭圆曲线的极大性,它们的自变群包含 Z/2Z×Z/2Z。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
On the Rosenhain forms of superspecial curves of genus two

In this paper, we examine superspecial genus-2 curves C:y2=x(x1)(xλ)(xμ)(xν) in odd characteristic p. As a main result, we show that the difference between any two elements in {0,1,λ,μ,ν} is a square in Fp2. Moreover, we show that C is maximal or minimal over Fp2 without taking its Fp2-form (we give an explicit criterion in terms of p that tells whether C is maximal or minimal). As an application, we also study the maximality of superspecial hyperelliptic curves of genera 3 and 4 whose automorphism groups contain Z/2Z×Z/2Z.

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来源期刊
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.
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