Properties that characterize Gaussian periods and cyclotomic numbers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

Properties that characterize Gaussian periods and cyclotomic numbers

Authors:	F Thaine

Institution:	Department of Mathematics and Statistics - CICMA, Concordia University, 1455, de Maisonneuve Blvd. W., Montreal, Quebec, Canada H3G 1M8

Abstract:	Let be a prime number, $\zeta _q$ a -th primitive root of 1 and $\eta _0,\dots ,\eta _{e-1}$ the periods of degree of $\mathbb{Q}(\zeta _q)$ . Write $\eta _0\eta _i=\sum _{j=0}^{e-1} a_{i,j}\eta _j$ with $a_{i,j}\in \mathbb{Z}$ . Several characterizations of the numbers $\eta _i$ and $a_{i,j}$ (or, equivalently, of the cyclotomic numbers of order ) are given in terms of systems of equations they satisfy and a condition on the linear independence, over $\mathbb{Q}$ , of the $\eta _i$ or on the irreducibility, over $\mathbb{Q}$ , of the characteristic polynomial of the matrix $a_{i,j}]_{0\leq i,j\leq e-1}$ .

Keywords:

	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