立方三折与非退化赫米提三折交点的最大点数

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-06-25 DOI:10.1016/j.ffa.2024.102462

Mrinmoy Datta , Subrata Manna

引用次数: 0

摘要

埃杜库（Edoukou）在 2008 年猜想，P4(Fq2) 中的非退化赫米提三重与定义在 Fq2 上的 d 度三重最多有 d(q5+q2)+q3+1 个共同点。他证明了 d=2 的猜想。在本文中，我们证明该猜想在 d=3 和 q≥7 时为真。

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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Maximum number of points on an intersection of a cubic threefold and a non-degenerate Hermitian threefold

It was conjectured by Edoukou in 2008 that a non-degenerate Hermitian threefold in $P^{4} (F_{q^{2}})$ has at most $d (q^{5} + q^{2}) + q^{3} + 1$ points in common with a threefold of degree d defined over $F_{q^{2}}$ . He proved the conjecture for $d = 2$ . In this paper, we show that the conjecture is true for $d = 3$ and $q \geq 7$ .

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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.