Families of irreducible polynomials of Gaussian periods and matrices of 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

Families of irreducible polynomials of Gaussian periods and matrices of cyclotomic numbers

Authors:	F. Thaine.

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

Abstract:	Given an odd prime we show a way to construct large families of polynomials $P_{q}(x)in mathbb{Q}[x]$ , , where is a set of primes of the form mod and $P_{q}(x)$ is the irreducible polynomial of the Gaussian periods of degree in $mathbb{Q}(zeta _{q})$ . Examples of these families when are worked in detail. We also show, given an integer and a prime mod , how to represent by matrices the Gaussian periods $eta _{0},dots ,eta _{n-1}$ of degree in $mathbb{Q}(zeta _{q})$ , and how to calculate in a simple way, with the help of a computer, irreducible polynomials for elements of $mathbb{Q}(eta _{0})$ .

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