Inhomogeneous Diophantine approximation with general error functions

Lingmin Liao; Michał Rams

Acta Arithmetica, Tome 161 (2013), p. 25-35 / Harvested from The Polish Digital Mathematics Library

Résumé

Let α be an irrational and φ: ℕ → ℝ⁺ be a function decreasing to zero. Let $ω (α) : = s u p θ \geq 1 : l i m i n f_{n \to \infty} n^{θ} | | n α | = 0$ $. F o r a n y α w i t h a g i v e n ω (α), w e g i v e s o m e s h a r p e s t i m a t e s f o r t h e H a u s d o r f f d i m e n s i o n o f t h e s e t$ $E_{φ} (α)$ := y ∈ ℝ: ||nα -y|| < φ(n) for infinitely many n, where ||·|| denotes the distance to the nearest integer.

Publié le : 2013-01-01

Zbl 1301.28006

EUDML-ID : urn:eudml:doc:279566

@article{bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-1-2,
     author = {Lingmin Liao and Micha\l\ Rams},
     title = {Inhomogeneous Diophantine approximation with general error functions},
     journal = {Acta Arithmetica},
     volume = {161},
     year = {2013},
     pages = {25-35},
     zbl = {1301.28006},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-1-2}
}

Lingmin Liao; Michał Rams. Inhomogeneous Diophantine approximation with general error functions. Acta Arithmetica, Tome 161 (2013) pp. 25-35. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-aa160-1-2/