Geometry and distribution of roots of ${\mu }^2\equiv D\mathrm{mod}m$ with $D\equiv 1\mathrm{mod}4$

Zonglin Li, Matthew Welsh

We extend the geometric interpretation of the roots of the quadratic congruence ${\mu }^2\equiv D(\mathrm{mod}m)$ as the tops of certain geodesics in the hyperbolic plane to the case when $D$…