Equidistribution conjecture for intersections of closed geodesics

About 7 years old · traced to

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 ℓ~q\tilde{\ell}_q arising from qq and forms of discriminant DD.

Intersection equidistribution conjecture. As D→∞D\rightarrow\infty, the multiset Iq(D)I_q(D) is equidistributed on ℓ~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.

References

Primary source

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

Progress summary

Never refreshed

Nothing recorded yet. Refresh searches the literature and the public web for attempts on this problem, and writes the first summary here.

Solutions 0

No solutions have been posted yet.