An elementary proof of the law of quadratic reciprocity over function fields期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

按检索

An elementary proof of the law of quadratic reciprocity over function fields

Authors:	Chun-Gang Ji Yan Xue

Institution:	Department of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China ; Department of Mathematics, Nanjing Normal University, Nanjing 210097, People's Republic of China

Abstract:	Let and be relatively prime monic irreducible polynomials in $\mathbb{F}_{q}T]$ ( $2\nmid q$ ). In this paper, we give an elementary proof for the following law of quadratic reciprocity in $\mathbb{F}_{q}T]$ : $\displaystyle \left (\frac{Q}{P}\right )\left (\frac{P}{Q}\right )=(-1)^{\frac{\vert P\vert-1}{2}\frac{\vert Q\vert -1}{2} },$ where $\left (\frac{Q}{P}\right )$ is the Legendre symbol.

Keywords:	Rational function fields Legendre symbol quadratic reciprocity law

	点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息
	点击此处可从《Proceedings of the American Mathematical Society》下载免费的PDF全文