On the discrepancy of uniformly distributed roots of quadratic congruences

In this paper we consider the distribution of fractional parts {ν/p}, where p is a prime less than or equal to x and ν is the root in Z/pZ of a quadratic polynomial with negative discriminant. This set is known to be uniformly distributed as x→∞. Here we apply the Erd?s-Turán inequality to obtain an estimate for the discrepancy.