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arXiv · 1508.01770

Badly approximable $S$-numbers and absolute Schmidt games

Dmitry Kleinbock·Tue Ly
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Abstract

Let $K$ be a number field, let $S$ be the set of all normalized, non-conjugate Archimedean valuations of $K$, and let $K_{S} = \prod_{v \in S} K_v$ be the Minkowski space associated with $K$. We strengthen recent results of \cite{EsdahlKristensen10} and \cite{EinsiedlerGhoshLytle13} by showing that the set of badly approximable elements of $K_S$ is $\mathcal{H}$-absolute winning for a certain family of subspaces of $K_{S}$.

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Dmitry Kleinbock, Tue Ly. 2015-08-07. Badly approximable $S$-numbers and absolute Schmidt games. https://arxiv.org/abs/1508.01770

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