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 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.
