Cycle integrals of the Parson Poincaré series and intersection angles of geodesics on modular curves
Volume 206 / 2022
Acta Arithmetica 206 (2022), 61-74
MSC: Primary 11F11; Secondary 11F67.
DOI: 10.4064/aa220314-13-10
Published online: 25 November 2022
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 Poincaré series, due to Katok. On the other hand, it extends a recent geometric formula of Matsusaka and of Duke, Imamoḡlu, and Tóth for the cycle integrals of weight 2 modular integrals.
