Polynomial effective density in quotient of SL₂(ℚ_p) × SL₂(ℚ_p)

2024/04/22 by Lin, Zuo
#37A17 #37A25 #Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2404.13931

Abstract

We prove an effective density theorem with polynomial error rate for orbits of upper triangular subgroup of SL₂(ℚ_p) in SL₂(ℚ_p) × SL₂(ℚ_p) for prime number p > 3. The proof is based on the use of Margulis function, a restricted projection theorem on ℚ_p³, and spectral gap of the ambient space.

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