Badly approximable S-numbers and absolute Schmidt games

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• 作者：Dmitry Kleinbock ^{kleinboc@brandeis.edu" class="auth_mail" title="E-mail the corresponding author} ; Tue Ly ; ^{lntue@brandeis.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Diophantine approximation ; Schmidt games ; Algebraic numbers ; Badly approximable
• 刊名：Journal of Number Theory
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：164
• 期：Complete
• 页码：13-42
• 全文大小：509 K

文摘

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 [ESK10] and [EGL15] by showing that the set of badly approximable elements of K_S$K_S$ is H$\mathcal{H}$-absolute winning for a certain family of subspaces of K_S$K_S$.