On the coefficients of cyclotomic polynomials

Let $\Phi\sb{n}(z)$ denote the $n$th cyclotomic polynomial, given by$\Phi\sb{n}(z) = {\prod\limits\sbsp{a=1\atop(a,n)=1}{n}} (z - \exp(2π ia/n)) = {\sum\limits\sbsp{m=0}{\phi(n)}} a(m,n)z\sp{m}.$It is easily verified that for $n > 1$ $\Phi\sb{n}(z)={\prod\limits\sb{d\vert n}}(1-z\sp{d})\sp{μ(n/d)},$where $\mu$ is the Moebius function. Hence the coefficients $a(m,n)$ of $\Phi\sb{n}(z)$ are integers, and for every fixed $m,\ a(m,n)$ assumes only finitely many possible values.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Discipline thesis:degree_discipline

Mathematics

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2011

Author dc:creator

• Bachman, Gennady

Contributors dc:contributor

• Hildebrand, A.J.

• Mathematics

Statement dc:rights

• Copyright 1991 Bachman, Gennady

Language dc:language

eng

Identifier

AAI9210733
(UMI)AAI9210733

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/23444