Character Sums and Primitive Roots in Algebraic Number Fields.
In this paper, we apply character sum estimates to study products of factorials modulo .
Let be a finite subset of an abelian group and let be a closed half-plane of the complex plane, containing zero. We show that (unless possesses a special, explicitly indicated structure) there exists a non-trivial Fourier coefficient of the indicator function of which belongs to . In other words, there exists a non-trivial character such that .