Cycle Integrals of the Parson Poincar\'e Series and Intersection Angles of Geodesics on Modular Curves
Number Theory
2022-03-17 v1
Abstract
We prove a geometric formula for the cycle integrals of Parson's weight 2k modular integrals in terms of the intersection angles of geodesics on modular curves. Our result is an analog for modular integrals of a classical formula for the cycle integrals of certain hyperbolic Poincar\'e series, due to Katok. On the other hand, it extends a recent geometric formula of Matsusaka and Duke, Imamo\={g}lu, and T\'oth for the cycle integrals of weight 2 modular integrals.
Keywords
Cite
@article{arxiv.2203.08526,
title = {Cycle Integrals of the Parson Poincar\'e Series and Intersection Angles of Geodesics on Modular Curves},
author = {Alessandro Lägeler and Markus Schwagenscheidt},
journal= {arXiv preprint arXiv:2203.08526},
year = {2022}
}