p-adic equidistribution of modular geodesics and of Heegner points on Shimura curves

2024/05/25 by Patricio Pérez-Piña, Pérez-Piña, Patricio
Mathematics · #11F85 (Secondary) #11G15 (Primary) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Dynamical Systems (math.DS) #FOS: Mathematics #Geometry and complex manifolds #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2405.16032

openalex publication_date 2024/05/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We propose a p-adic version of Duke's Theorem on the equidistribution of closed geodesics on modular curves. Our approach concerns quadratic fields split at p as well as a p-adic covering of the modular curve. We also prove an equidistribution result of Heegner points in the p-adic space attached to Shimura curves.

Related

• Equidistribution of CM points on Shimura Curves and ternary theta series
• The distribution of closed geodesics on the modular surface, and Duke's theorem
• Equidistribution of CM points on a Shimura Curve modulo a ramified prime
• p-adic Eichler-Shimura maps for the modular curve
• p-adic Gross-Zagier Formula for Heegner Points on Shimura Curves over Totally Real Fields