Equidistribution conjecture for intersections of closed geodesics

Let qq be a fixed PIBQF, let DD be a discriminant, and let Iq(D)I_q(D) be the multiset of intersection points on the closed geodesic ~q\tilde{\ell}_q arising from qq and forms of discriminant DD.

Intersection equidistribution conjecture. As DD\rightarrow\infty, the multiset Iq(D)I_q(D) is equidistributed on ~q\tilde{\ell}_q with respect to the hyperbolic metric.

This conjecture concerns the distribution of intersections of a fixed closed geodesic with geodesics associated to forms of growing discriminant. It was resolved by Junehyuk Jung and Naser Sardari.

Sources & referencesView supporting material

Primary source

James Rickards, “Computing intersections of closed geodesics on the modular curve”, arXiv:1909.04103 (2021).

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