# 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 ?
Throughout this work we assume that if p [member of] I then p is not a root of unity, so that we always have [I.
We remind the reader that if p [member of] I then we assume that p is not a root of unity.
for every [theta]-function [theta](q) there is some root of unity [zeta] for which difference f(q) - [theta](q) is unbounded as q [right arrow] [zeta] radially.
A triple (X, X(q), C) consisting of a finite set X, a polynomial X(q) [member of] N[q] satisfying X(1) = [absolute value of X], and a cyclic group C acting on X exhibits the cyclic sieving phenomenon if, for every c [member of] C, if w is a primitive root of unity of the same multiplicative order as c, then
Let K be the field of complex numbers C and q be a primitive Nth root of unity, where N [greater than or equal to] 2.
The equation F([omega]) = 0 is an algebraic equation with rational coefficients in the unknown (omega); hence, if some primitive d-th root of unity satisfies it, then every primitive d-th root of unity satisfies it.
Fix once and for all a primitive nth root of unity [zeta].
When q is a root of unity, its image under the specialization [bar.
th] root of unity in a field F of characteristic zero (so necessarily l [greater than or equal to] 2).
n] -th root of unity [MATHEMATICAL EXPRESSION NOT REPRODUCIBLE IN ASCII] (Thm.
We assume that K contains a primitive [absolute value of G]-th root of unity and that k is algebraically closed.

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