Liminf Sets in Simultaneous Diophantine Approximation

Faustin Adiceam

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arXiv · 1308.3806

Liminf Sets in Simultaneous Diophantine Approximation

Faustin Adiceam

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Abstract

Let Q be an infinite set of positive integers. Denote by W(Q) the set of n-tuples of real numbers simultaneously tau-well approximable by infinitely many rationals with denominators in Q but only by finitely many rationals with denominators in the complement of Q. The Hausdorff dimension of the liminf set W(Q) is computed when tau > 2 + 1/n. A p-adic analogue of the problem is also studied.

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Faustin Adiceam. 2013-08-17. Liminf Sets in Simultaneous Diophantine Approximation. https://arxiv.org/abs/1308.3806

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