Margulis' Inequality for translates of horospherical orbits and applications to equidistribution

2023/09/29 by Katz, Asaf · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2310.00169

Abstract

In this paper we develope a quantitative non-divergence theorem for translates of horospherical orbits, using the technique of Margulis' inequality as developed by Eskin-Margulis-Mozes and Eskin-Margulis. As we use the Margulis' inequality, our results do not depend on the spectral gap of the action. As an application of our techniques, we show that given a horospherical flow over the space of lattices, the horospherical orbit of every lattice defined over a number field, not contained in a proper rational parabolic subgroup is equidistributed with an effective rate.

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