Distribution of Roots of Polynomial Congruences

For a prime p, we obtain an upper bound on the discrepancy offractions r/p, where r runs through all of roots modulo p of all monicunivariate polynomials of degree d whose vector of coefficients belongsto a d-dimensional box ℬ. The bound is nontrivial starting with boxesℬ of size |ℬ|≥pd/2+ɛ for any fixed ɛ<0 and sufficiently large p