Effective rational approximation on spheres

Zouhair Ouaggag

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arXiv · 2206.08924

Effective rational approximation on spheres

Zouhair Ouaggag

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Abstract

We prove an effective estimate for the counting function of Diophantine approximants on the sphere S$^n$. 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.

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Zouhair Ouaggag. 2022-06-17. Effective rational approximation on spheres. https://arxiv.org/abs/2206.08924

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