root of unity

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root of unity

[¦rüt əv ′yü·nəd·ē]
(mathematics)
A root of unity in a field F is an element a in F such that a n = 1 for some positive integer n.
References in periodicals archive ?
This is done using the classical cyclotomic polynomials [[PHI].
n] is admissible if and only if the cyclotomic polynomial [[PHI].
The computation of the cyclotomic polynomial [[PHI].
Thus it suffices to interpret the coefficients of cyclotomic polynomials for squarefree n.
They also thank Sam Elder, Nathan Kaplan, and Pieter Moree for helpful references on cyclotomic polynomials.
Bachman, On the Coefficients of Cyclotomic Polynomials Memoirs of the American Mathematical Society 106, 1993.
Elder, Flat Cyclotomic Polynomials, Colorado Math Circle Talk, January 2, 2010, http://www.
Kaplan, Flat cyclotomic polynomials of order three.
29] Zhao, Jia; Zhang, Xianke, Coefficients of ternary cyclotomic polynomials.
This paper studies the cyclotomic polynomial [[PHI].
Section 2 describes our first interpretation for the cyclotomic polynomial, which applies much more generally to any monic polynomial in Z[x].
The special case where f(x) is the cyclotomic polynomial [[PHI].