Badly approximable vectors in affine subspaces: Jarn'ık-type result

2011/02/22 by Moshchevitin, Nikolay
#11J13 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1102.4431

Abstract

Consider irrational affine subspace A⊂ ℝ^d of dimension a. We prove that the set \ξ=(ξ₁,...,ξ_d) ∈ A: q^1/a⋅ max_{1≤ i ≤ d} ||qξ_i|| → ∞, q→ ∞\ is an α-winning set for every α∈ (0,1/2]

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