Cyclotomic problem, Gauss sums and Legendre curve
Cyclotomic problem, Gauss sums and Legendre curve作者机构：Department of Mathematical Sciences Tsinghua University Department of Basic Courses Beijing Union University
出 版 物：《Science China Mathematics》 (中国科学：数学（英文版）)
年 卷 期：2013年第56卷第7期
页 面：1485-1508页
核心收录：
学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学]
基 金：supported by National Natural Science Foundation of China(Grant Nos.10990011,11001145 and 61170289) the Science and Technology on Information Assurance Laboratory Foundation(Grant No.KJ-12-01)
主 题：cyclotomic number cyclotomic problem Gauss sums Jacobi sums Legendre curve
摘 要：In this paper, explicit determination of the cyclotomic numbers of order l and 2l, for odd prime l ≡ 3 (mod 4), over finite field Fq in the index 2 case are obtained, utilizing the explicit formulas on the corresponding Gauss sums. The main results in this paper are related with the number of rational points of certain elliptic curve, called Legendre curve, and the properties and value distribution of such number are also presented.
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