Liminf Sets in Simultaneous Diophantine Approximation

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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.
Original languageEnglish
Pages (from-to)461-483
Number of pages22
JournalJournal de Théorie des Nombres de Bordeaux
Issue number2
Publication statusPublished - 2016

Bibliographical note

This is an author produced version of a paper accepted for publication in Journal de Théorie des Nombres de Bordeaux. Uploaded with permission from the publisher.


  • math.NT
  • 11J83, 11K60

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