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Abstract Let be a ‐tuple of positive real numbers such that and . A ‐dimensional vector is said to be ‐singular if for every , there exists such that for all , the system of inequalities has an integer solution . We prove that the Hausdorff dimension of the set of ‐singular vectors in is bounded below by . Our result partially extends the previous result of Liao et al. Hausdorff dimension of weighted singular vectors in , J. Eur. Math. Soc. 22 (2020), 833–875.
Kim et al. (Tue,) studied this question.
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