An upper bound of the Hausdorff dimension of singular vectors on affine subspaces

In Diophantine approximation, the notion of singular vectors was introduced by Khintchine in the 1920's. We study the set of singular vectors on an affine subspace of \(\mathbb{R}^n\). We give an upper bound of its Hausdorff dimension in terms of the Diophantine exponent of the parameter of the...

Full description

Saved in:
Bibliographic Details
Published inarXiv.org
Main Authors Shah, Nimish A, Yang, Pengyu
Format Paper Journal Article
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 10.11.2023
Subjects
Mathematics - Dynamical Systems
Mathematics - Number Theory
Subspaces
Upper bounds
Online AccessGet full text

Cover

More Information
Summary:In Diophantine approximation, the notion of singular vectors was introduced by Khintchine in the 1920's. We study the set of singular vectors on an affine subspace of \(\mathbb{R}^n\). We give an upper bound of its Hausdorff dimension in terms of the Diophantine exponent of the parameter of the affine subspace.
ISSN:2331-8422
DOI:10.48550/arxiv.2311.05834