Notes on the Distribution of Roots Modulo a Prime of a Polynomial II

Abstract

Abstract Let f (x) be a monic polynomial with integer coefficients and 0 ≤ r 1 ≤ ··· ≤ r n <p its roots modulo a prime p. We generalize a conjecture on the distribution of roots r i with additional congruence relations r i ≡ R i mod L from the case that f has no non-trivial linear relation among roots to the case that f has a non-trivial linear relation.