Fractional dimension related to badly approximable matrices associated with higher successive minima
Number Theory
2023-01-02 v1 Classical Analysis and ODEs
Abstract
In this article we introduce the notion of badly approximable matrices of higher order using higher sucessive minima in . We prove that for order less than , they have Lebesgue measure zero and the gaps between them still have full Hausdorff dimension.
Cite
@article{arxiv.2212.14436,
title = {Fractional dimension related to badly approximable matrices associated with higher successive minima},
author = {Hao Xing},
journal= {arXiv preprint arXiv:2212.14436},
year = {2023}
}
Comments
arXiv admin note: text overlap with arXiv:1901.06602 by other authors