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arXiv · 1912.13070

Singular vectors on manifolds and fractals

Dmitry Kleinbock·Nikolay Moshchevitin·Barak Weiss
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Abstract

We generalize Khintchine's method of constructing totally irrational singular vectors and linear forms. The main result of the paper shows existence of totally irrational vectors and linear forms with large uniform Diophantine exponents on certain subsets of $\mathbb{R}^n$, in particular on any analytic submanifold of $\mathbb{R}^n$ of dimension $\ge 2$ which is not contained in a proper rational affine subspace.

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Dmitry Kleinbock, Nikolay Moshchevitin, Barak Weiss. 2019-12-30. Singular vectors on manifolds and fractals. https://arxiv.org/abs/1912.13070

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