Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds
Number Theory
2026-02-12 v1 Classical Analysis and ODEs
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.
Cite
@article{arxiv.2602.11012,
title = {Rational Points in Hyperbolic Regions and Multiplicative Diophantine Approximation on Manifolds},
author = {Sam Chow and Rajula Srivastava and Niclas Technau and Han Yu},
journal= {arXiv preprint arXiv:2602.11012},
year = {2026}
}
Comments
45 pages, comments welcome