On roots of quadratic congruences

Hieu T. Ngo

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arXiv · 2107.13301

On roots of quadratic congruences

Hieu T. Ngo

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Abstract

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. T\'oth 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.

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Hieu T. Ngo. 2021-07-28. On roots of quadratic congruences. https://arxiv.org/abs/2107.13301

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