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.

Let [xi] be a primitive m-th

root of unity, and [[mu].

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.