Liminf Sets in Simultaneous Diophantine Approximation
Number Theory
2013-08-20 v1
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.
Cite
@article{arxiv.1308.3806,
title = {Liminf Sets in Simultaneous Diophantine Approximation},
author = {Faustin Adiceam},
journal= {arXiv preprint arXiv:1308.3806},
year = {2013}
}