Weighted Diophantine approximation on manifolds
Number Theory
2026-02-12 v1 Dynamical Systems
Abstract
We establish a weighted simultaneous Khintchine-type theorem, both convergence and divergence, for all nondegenerate manifolds, which answers a problem posed in [Math. Ann., 337(4):769-796, 2007]. This extends the main results of [Acta Math., 231:1-30, 2023] and [Ann. of Math. (2), 175(1):187-235, 2012] in the weighted set-up. As a by-product of our method, we also obtain a multiplicative Khintchine-type convergence theorem for all nondegenerate manifolds, which is a simultaneous analogue of the celebrated result of Bernik, Kleinbock, and Margulis for dual approximation.
Cite
@article{arxiv.2602.11045,
title = {Weighted Diophantine approximation on manifolds},
author = {Victor Beresnevich and Shreyasi Datta and Lei Yang},
journal= {arXiv preprint arXiv:2602.11045},
year = {2026}
}
Comments
31 pages