Ultrametric Logarithm Laws I

2005/06/26 by Jayadev S. Athreya, Athreya, Jayadev S., Anish Ghosh +3 · 1 citation
Computer Science · Mathematics · #327A17 (Primary) 11H16 (Secondary) #Dynamical Systems (math.DS) #FOS: Mathematics #Geometric Topology (math.GT) #Mathematical Dynamics and Fractals #Topological and Geometric Data Analysis #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.math/0506531

openalex publication_date 2005/06/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We announce ultrametric analogues of the results of Kleinbock-Margulis for shrinking target properties of semisimple group actions on symmetric spaces. The main applications are S-arithmetic Diophantine approximation results and logarithm laws for buildings, generalizing the work of Hersonsky-Paulin on trees.

Cited by

• Vertex volumes, lattice-minima tails, and height zeta functions for the standard arithmetic quotient of PGL_d

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