Year: 2013
Type: preprint
Abstract: We define two-dimensional Dirichlet spectrum (with respect to Euclidean norm) as D_2=λ\in\mathbf{R} | \exists \mathbf{v}=(v_1,v_2)\in \mathbf {R}^2: \limsup\limits_{t\rightarrow\infty} {t\cdotψ_{v}^2(t)}=λ, where ψ_{v}(t)=\min\limits_{1\leqslant q\leqslant t}\sqrt{|q v_1|^2+|q v_2|^2} is the two-dimensional "irrationality measure function". Our main result states the equality D_2=[0; 2/sqrt{3}].
Source: arXiv (Cornell University)
Authors: Akhunzhanov, Renat, Shatskov, Denis
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2213052011