Work

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

Year: 2024

Type: article

Abstract: 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 R n \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.

Source: Transactions of the American Mathematical Society Series B

DOI: 10.1090/btran/212

Authors: Nimish Shah, Pengyu Yang

Institutions: The Ohio State University, Chinese Academy of Sciences

Language: English

Topic: Mathematical Dynamics and Fractals

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $2,750

Funders: National Natural Science Foundation of China, National Key Research and Development Program of China