2021/07/28 by Hieu T. Ngo, Ngo, Hieu T.
Mathematics · #Advanced Mathematical Identities #Analytic Number Theory Research #FOS: Mathematics #Mathematics and Applications #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2107.13301
openalex publication_date 2021/07/28 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The equidistribution of roots of quadratic congruences with prime moduli depends crucially upon effective bounds for a special Weyl linear form. Duke, Friedlander and Iwaniec discovered a strong estimate for this Weyl linear form when the quadratic polynomial has negative discriminant. Tóth established an analogous but weaker bound when the quadratic polynomial has positive discriminant. We obtain a stronger estimate for the Weyl linear form for quadratics of positive discriminants.