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arXiv · 2602.11045

Weighted Diophantine approximation on manifolds

Victor Beresnevich·Shreyasi Datta·Lei Yang
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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.

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Victor Beresnevich, Shreyasi Datta, Lei Yang. 2026-02-11. Weighted Diophantine approximation on manifolds. https://arxiv.org/abs/2602.11045

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