On the cyclotomic field Q(e2πi/p) and Zhi-Wei Sun's conjecture on det Mp

IF 1.2 3区数学 Q1 MATHEMATICS

Finite Fields and Their Applications Pub Date : 2024-10-31 DOI:10.1016/j.ffa.2024.102533

Li-Yuan Wang , Hai-Liang Wu

引用次数: 0

Abstract

In 2019, Zhi-Wei Sun posed an interesting conjecture on certain determinants with Legendre symbol entries. In this paper, by using the arithmetic properties of p-th cyclotomic field and the finite field

F_{p}

, we confirm this conjecture.

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关于回旋场 Q(e2πi/p) 和孙志伟关于 det Mp 的猜想

2019 年，孙志伟提出了一个关于某些具有 Legendre 符号项的行列式的有趣猜想。本文利用 p-th 回旋域和有限域 Fp 的算术性质，证实了这一猜想。

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.

On the cyclotomic field Q(e2πi/p) and Zhi-Wei Sun's conjecture on det Mp

Abstract

On the cyclotomic field Q(e2πi/p) and Zhi-Wei Sun's conjecture on det Mp