Distribution of roots of polynomials congruences

For a prime p, we obtain an upper bound on the discrepancy of fractions r/p, where r runs through all of roots modulo p of all monic univariate polynomials of degree d whose vector of coefficients belongs to a d-dimensional box ℬ. The bound is nontrivial starting with boxes ℬ of size |ℬ| ≥ pd/²⁺ε for any fixed ε < 0 and sufficiently large p.5 page(s