2013/08/17 by Faustin Adiceam, Adiceam, Faustin
Mathematics · #11J83 #11K60 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11J83 #msc:11K60
paper · pdf · doi:10.48550/arxiv.1308.3806
arxiv created 2013/08/17 · arxiv updated 2013/08/20
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.