English

Two-dimensional badly approximable vectors and Schmidt's game

Number Theory 2016-02-10 v2

Abstract

We prove that for any pair (s,t)(s,t) of nonnegative numbers with s+t=1s+t=1, the set of two-dimensional (s,t)(s,t)-badly approximable vectors is winning for Schmidt's game. As a consequence, we give a direct proof of Schmidt's conjecture using his game.

Keywords

Cite

@article{arxiv.1204.3610,
  title  = {Two-dimensional badly approximable vectors and Schmidt's game},
  author = {Jinpeng An},
  journal= {arXiv preprint arXiv:1204.3610},
  year   = {2016}
}

Comments

12 pages

R2 v1 2026-06-21T20:50:20.651Z