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一类高斯和显式公式的直接求法

Explicit Determination of Certain Kinds of Gauss Sums
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摘要 本文讨论了指数2情形下的一类阶数为偶数的高斯和.异于现有的方法,不借助其他指数2情形高斯和的结果,直接利用Stickelberger理想分解定理得到了相应高斯和的显式计算公式. This paper deduces the explicit formulas of a kind of Gauss sums with even order in the index 2 case. Note that the method of proof in this paper is directly exploiting Stickelberger's theorem, which indicates that our results are independent of the known results of any other Gauss sums in the index 2 case.
出处 《数学进展》 CSCD 北大核心 2014年第2期255-262,共8页 Advances in Mathematics(China)
基金 国家自然科学基金(No.11371011) 北京市自然科学基金(No.1144012) 北京市教委面上项目(No.SQKM201411417009) 信息保障技术重点实验室开放基金(No.KJ-13-005) 北京联合大学新起点计划项目(No.ZK201218)
关键词 高斯和 显式计算 指数2情形 Stickelberger理想分解定理 Davenport—Hasse提升 定理 Gauss sum explicit determination index 2 case Stickelberger's theorem Davenport-Hasse (lift) theorem
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参考文献1

  • 1YANG Jing1,2 & XIA LingLi3,1Department of Mathematical Sciences,Tsinghua University,Beijing 100084,China,2Division of Mathematical Sciences,School of Physical and Mathematical Sciences,Nanyang Technological University,637371,Singapore,3Basic Courses Department,Beijing Union University,Beijing 100101,China.Complete solving of explicit evaluation of Gauss sums in the index 2 case[J].Science China Mathematics,2010,53(9):2525-2542. 被引量:5

二级参考文献20

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