Inhomogeneous Diophantine approximation with general error functions

Lingmin Liao, and Michał Rams. "Inhomogeneous Diophantine approximation with general error functions." Acta Arithmetica 160.1 (2013): 25-35. <http://eudml.org/doc/279566>.

@article{LingminLiao2013,
abstract = {Let α be an irrational and φ: ℕ → ℝ⁺ be a function decreasing to zero. Let $ω(α):= sup \{θ ≥ 1: lim inf_\{n→ ∞\}n^\{θ\} ||nα\}|=0$$. For any α with a given ω(α), we give some sharp estimates for the Hausdorff dimension of the set $$E_\{φ\}(α)$ := y ∈ ℝ: ||nα -y|| < φ(n) for infinitely many n, where ||·|| denotes the distance to the nearest integer.},
author = {Lingmin Liao, Michał Rams},
journal = {Acta Arithmetica},
keywords = {inhomogeneous Diophantine approximations; Hausdorff dimension},
language = {eng},
number = {1},
pages = {25-35},
title = {Inhomogeneous Diophantine approximation with general error functions},
url = {http://eudml.org/doc/279566},
volume = {160},
year = {2013},
}

TY - JOUR
AU - Lingmin Liao
AU - Michał Rams
TI - Inhomogeneous Diophantine approximation with general error functions
JO - Acta Arithmetica
PY - 2013
VL - 160
IS - 1
SP - 25
EP - 35
AB - Let α be an irrational and φ: ℕ → ℝ⁺ be a function decreasing to zero. Let $ω(α):= sup {θ ≥ 1: lim inf_{n→ ∞}n^{θ} ||nα}|=0$$. For any α with a given ω(α), we give some sharp estimates for the Hausdorff dimension of the set $$E_{φ}(α)$ := y ∈ ℝ: ||nα -y|| < φ(n) for infinitely many n, where ||·|| denotes the distance to the nearest integer.
LA - eng
KW - inhomogeneous Diophantine approximations; Hausdorff dimension
UR - http://eudml.org/doc/279566
ER -