This chapter consists of elementary number theory and deals with the greatest common divisor, the euclidean algorithm, congruences, linear equations, primitive roots, and the quadratic reciprocity law. The material covered here corresponds to the first four chapters of Gauss's Disquisitiones arithmeticae...
In the quadratic case, the analytic proof of the reciprocity law for a numbr field involves a connection between Gauss-Hecke sums and theta constants or Thetanullwerte. We propose a generalization of Gauss-Hecke sums to higher degrees and discuss some aspects of the problem of determining higher...
这书可以说是数论第一本有系统的著作,高斯第一次介绍“同余”(Congrudent)这个概念(现在的中学“新数学”就有教这玩意儿)。而且还有数论上很重要的高斯称为“数论的酵母”的“二次互逆定理”(Law of Quadratic reciprocity)。这定理是描述一对素数的美丽关系,欧拉和勒让得知道这些关系,但没有法子证明。高斯在18...
Gauss also made important contributions to number theory with his 1801 bookDisquisitiones arithmeticae, which contained a clean presentation of modular arithmetic and the first proof of the law of quadratic reciprocity. He had been supported by a stipend from the Duke of Brunswick, but he did not ...
his published works were enough to establish his reputation as one of the greatest mathematicians of all time. Gauss early discovered the law of quadratic reciprocity and, independently of Legendre, the method of least squares. He showed that a regular polygon ofnsides can be constructed using onl...
–Quadratic Reciprocity Law; –at 21 wrote the Number Theory masterpiece“Disquisitiones Arithmeticae” (Latin, Arithmetical Investigations). Nephew and Maternal Uncle July 3, 2013tomcircleChinese,Education1 Comment There is a common proverb in my Chinese dialect Fujian spoken today in China Fujian pro...
GUO Xiang-rong (Department of Mathematics and Information Science, Tangshan Teachers College, Tangshan 063000, China) Abstract: The main content of this article is to introduce the application of the Legendre symbol to prove Gauss quadratic reciprocity law, part of which is not seen in the ...
Finally, Gauss Lemma and Law of Quadratic Reciprocity are proven.MML identifier: INT 5, version: 7.8.05 4.89.993 In this paper, we defined the quadratic residue and proved its fundamental properties on the base of some useful theorems. Then we defined the Legendre symbol and proved its ...
而且还有数论上很重要的高斯称为“数论的酵母”的“二次互逆定理”(Law of Quadratic reciprocity)。这定理是描述一对素数的美丽关系,欧拉和勒让得知道这些关系,但没有法子证明。高斯在18岁时重新发现并给了第一个证明,他认为这是数论的“宝石”,一生给出五个不同证明。 在天文学上的卓越贡献 24岁开始,高斯...
1. What is a Reciprocity Law?[J].B. F. Wyman,The American mathematical monthly.1972,第6期 2. 数论导引[M].华罗庚.1975 3. 解析数论基础[M].潘承洞; 潘承彪; 著.1991 上一页 1 下一页 相似文献 中文文献 外文文献 专利 1. Legendre符号及Gauss二次互反律的证明 [J] . 郭向荣...