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arXiv · 2006.10790

Quantitative non-divergence and lower bounds for points with algebraic coordinates near manifolds

Alessandro Pezzoni
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Abstract

Point counting estimates are a key stepping stone to various results in metric Diophantine approximation. In this paper we use the quantitative non-divergence estimates originally developed by Kleinbock and Margulis to improve lower bounds by Bernik, G\"{o}tze et al. for the number of points with algebraic conjugate coordinates close to a given manifold. In the process, we also improve on a Khinchin-Groshev-type theorem for a problem of constrained approximation by polynomials.

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Alessandro Pezzoni. 2020-06-18. Quantitative non-divergence and lower bounds for points with algebraic coordinates near manifolds. https://arxiv.org/abs/2006.10790

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