Singular vectors on manifolds and fractals

Dmitry Kleinbock, Nikolay Moshchevitin, Barak Weiss

Research output: Contribution to journalArticlepeer-review

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 ℝn, in particular on any analytic submanifold of ℝn of dimension ≥2 which is not contained in a proper rational affine subspace.

Original languageEnglish
Pages (from-to)589-613
Number of pages25
JournalIsrael Journal of Mathematics
Volume245
Issue number2
DOIs
StatePublished - 1 Oct 2021
Externally publishedYes

ASJC Scopus subject areas

  • Mathematics (all)

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