{"title":"Note on the Number of Solutions of Cubic Diagonal Equations over Finite Fields","authors":"Shuangnian HU, Shihan WANG, Yanyan LI, Yujun NIU","doi":"10.1051/wujns/2023285369","DOIUrl":null,"url":null,"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.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"2023-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wuhan University Journal of Natural Sciences","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1051/wujns/2023285369","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Multidisciplinary","Score":null,"Total":0}
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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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.
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