Badly approximable S-numbers and absolute Schmidt games

2015/08/07 by Kleinbock, Dmitry, Ly, Tue
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1508.01770

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 = ∏_{v ∈ S} K_v be the Minkowski space associated with K. We strengthen recent results of \citeEsdahlKristensen10 and \citeEinsiedlerGhoshLytle13 by showing that the set of badly approximable elements of K_S is H-absolute winning for a certain family of subspaces of K_S.

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