arXiv math/05065312005-06math.GTmath.DS

Ultrametric Logarithm Laws I

Jayadev S. Athreya, Anish Ghosh, Amritanshu Prasad

备注：: This announcement has been completely revised to reflect many new developments. Please direct all references to this NEW announcement. It is now co-authored work. Submitted to Discrete and Continuous Dynamical Systems

英文摘要：

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.

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