The winning property of mixed badly approximable numbers

Yaqiao Li

The winning property of mixed badly approximable numbers

Number Theory 2013-12-06 v2

Authors: Yaqiao Li

Abstract

For any pair of real numbers $(i,j)$ with $0<i,j<1$ and $i+j=1$ , we prove that the set of $p$ -adic mixed $(i,j)$ -badly approximable numbers $\bad_p(i, j)$ is 1/2-winning in the sense of Schmidt's game. This improves a recent result of Badziahin, Levesley, and Velani on mixed Schmidt conjecture.

Keywords

mixed badly approximable numbers Schmidt's game winning set p-adic numbers Diophantine approximation Schmidt conjecture

Cite

@article{arxiv.1212.6584,
  title  = {The winning property of mixed badly approximable numbers},
  author = {Yaqiao Li},
  journal= {arXiv preprint arXiv:1212.6584},
  year   = {2013}
}

Comments

5 pages. Moscow Journal of Combinatorics and Number Theory, vol. 3, iss. 3(2013), accepted

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