English

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 Rd\mathbb R^d. We prove that for order less than dd, they have Lebesgue measure zero and the gaps between them still have full Hausdorff dimension.

Keywords

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