Effective rational approximation on spheres

2022/06/17 by Zouhair Ouaggag, Ouaggag, Zouhair · 1 citation
Mathematics · #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT

paper · pdf · doi:10.48550/arxiv.2206.08924

arxiv created 2022/06/17 · arxiv updated 2022/06/20

Abstract

We prove an effective estimate for the counting function of Diophantine approximants on the sphere Sⁿ. We use homogeneous dynamics on the space of orthogonal lattices, in particular effective equidistribution results and non-divergence estimates for the Siegel transform, developping on recent results of Alam-Ghosh and Kleinbock-Merrill.

Cited by

• Integrability of Siegel transforms and an application

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