Singular vectors on manifolds and fractals

DOI10.1007/S11856-021-2220-3arXiv1912.13070MaRDI QIDQ6332028

Nikolay Moshchevitin, Barak Weiss, Dmitry Kleinbock

Publication date: 30 December 2019

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 $ge2$ which is not contained in a proper rational affine subspace.

Mathematics Subject Classification ID

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