A spherical extension theorem and applications in positive characteristic

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-10-10 DOI:10.1016/j.ffa.2024.102515

Doowon Koh , Thang Pham

引用次数: 0

Abstract

In this paper, we prove an extension theorem for spheres of square radii in

F_{q}^{d}

, which improves a result obtained by Iosevich and Koh [9] (2010). Our main tool is a new point-hyperplane incidence bound which will be derived via a cone restriction theorem due to the authors and Lee (2022). Applications on the distance problems will be also discussed.

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正特征球面扩展定理及其应用

在本文中，我们证明了 Fqd 中方形半径球面的扩展定理，它改进了 Iosevich 和 Koh [9] (2010) 所获得的结果。我们的主要工具是一个新的点-超平面入射界限，它将通过作者和 Lee (2022) 提出的圆锥限制定理得到。我们还将讨论它在距离问题上的应用。

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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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.