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Showing 1 to 2 of 2 for “"Cyclotomic Polynomials"”.
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On the coefficients of cyclotomic polynomials
Let $\Phi\sb{n}(z)$ denote the $n$th cyclotomic polynomial, given by$$\Phi\sb{n}(z) = {\prod\limits\sbsp{a=1\atop(a,n)=1}{n}}\ (z - \exp(2\pi ia/n)) = {\sum\limits\sbsp{m=0}{\phi(n)}} a(m,n)z\sp{m}.$$It is easily verified that for $n > 1$ $$\Phi\sb{n}(z)={\prod\limits\sb{d\vert …
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Explicit Factorization of Generalized Cyclotomic Polynomials of Order $2^m 3$ Over a Finite Field $F_q$
We give explicit factorizations of $a$-cyclotomic polynomials of order $2^m 3$, $Q_{2^m3,a}(x)$, over a finite field $F_q$ with $q$ elements where $q$ is a prime power, $m$ is a nonnegative integer and $a$ is a nonnegative element of $F_q$. We use the relation between usual cyclotomic polynomials …