Notes on the Distribution of Roots Modulo a Prime of a Polynomial V: Weyl’s Criterion

Let f(x) be a monic integral polynomial of degree n and p a prime number, for which f(x) is fully decomposable modulo p. Let r1,…,rn be the roots of f(x)modp with 0≤r1≤⋯≤rn<p. We have conjectured that the sequence of (r1,…,rn)/p is uniformly distributed in some sense. We provide a clear explanation of this and generalize the Weyl criterion.