Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds

arXiv (Cornell University) 2026 Preprint Open access

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Authors: Sam Chow, Rajula Srivastava, Niclas Technau, Han Yu
DOI: 10.48550/arxiv.2602.11012
Cited by: 0

Abstract

We establish the convergence theory of multiplicative Diophantine approximation for all non-degenerate, smooth manifolds. We also settle said convergence theory for all affine subspaces satisfying a highly generic and essentially optimal Diophantine condition. This answers a question of Beresnevich and Velani from 2005, while simultaneously sharpening results of Kleinbock and Margulis on the strong extremality of non-degenerate manifolds, and of Kleinbock on the strong extremality of affine subspaces.

Fields of Study & Subjects

Mathematical Dynamics and Fractals Analytic Number Theory Research Algebraic Geometry and Number Theory

Publication details

Journal / source
arXiv (Cornell University)
Publication date
11 February 2026
Language
EN
Document type
Preprint