The winning property of mixed badly approximable numbers

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.

arXiv comment5 pages. Moscow Journal of Combinatorics and Number Theory, vol. 3, iss. 3(2013), accepted

References in corpus (3)

• Badziahin-Pollington-Velani's theorem and Schmidt's game
• On some open problems in Diophantine approximation
• The mixed Schmidt conjecture in the theory of Diophantine approximation

Cited by in corpus (2)

• On some open problems in Diophantine approximation
• On a mixed Khintchine problem in Diophantine approximation