Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields

Q3 Multidisciplinary

Wuhan University Journal of Natural Sciences Pub Date : 2023-10-01 DOI:10.1051/wujns/2023285369

Shuangnian HU, Shihan WANG, Yanyan LI, Yujun NIU

引用次数: 0

Abstract

Let [see formula in PDF] be the finite field, [see formula in PDF], with [see formula in PDF] being a prime and [see formula in PDF] being a positive integer. Let [see formula in PDF] be the multiplicative group of [see formula in PDF], that is [see formula in PDF]. In this paper, by using the Jacobi sums and an analog of Hasse-Davenport theorem, an explicit formula for the number of solutions of cubic diagonal equation [see formula in PDF] over [see formula in PDF] is given, where [see formula in PDF] and [see formula in PDF]. This extends earlier results.

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有限域上三次对角方程解的个数

设[见PDF中的公式]为有限域，[见PDF中的公式]为素数，[见PDF中的公式]为正整数。设[见PDF中的公式]为[见PDF中的公式]的乘法群，即[见PDF中的公式]。本文利用Jacobi和和类似于Hasse-Davenport定理，给出了三次对角方程(见公式)/(见公式)的解的显式公式，其中[见公式]和[见公式]。这扩展了之前的结果。

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

Wuhan University Journal of Natural Sciences Multidisciplinary-Multidisciplinary

CiteScore

0.40

自引率

0.00%

发文量

2485

期刊介绍： Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.