Badly approximable vectors in affine subspaces: Jarník-type result

Details Badly approximable vectors in affine subspaces: Jarník-type result Badly approximable vectors in affine subspaces: Jarník-type result

2011-02-22

arxiv.org/abs/1102.4431v1

Mathematics

Number Theory

6 pages

Scientific paper

Consider irrational affine subspace $ A\subset \mathbb{R}^d$ of dimension
$a$. We prove that the set $$ \{\xi =(\xi_1,...,\xi_d) \in {A}:\,\,\, \
q^{1/a}\cdot \max_{1\le i \le d} ||q\xi_i|| \to \infty,\,\,\,\, q\to \infty\}
$$ is an $\alpha$-winning set for every $\alpha \in (0,1/2]$

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