Hausdorff measure of sets of Dirichlet non-improvable affine forms
Sign Up to like & getrecommendations! Published in 2022 at "Advances in Mathematics"
DOI: 10.1016/j.aim.2022.108353
Abstract: For a non-increasing real valued function $\psi$, a pair $(A,\mathbf{b})$ of a real $m\times n$ matrix $A$ and $\mathbf{b}\in\mathbb{R}^m$ is said to be $\psi$-Dirichlet improvable if the system $$\|A\mathbf{q}+\mathbf{b}-\mathbf{p}\|^m < \psi(T)\quad\text{and}\quad\|\mathbf{q}\|^n < T$$ has a… read more here.
Keywords: dirichlet non; hausdorff measure; non improvable; mathbf ... See more keywords
Sets of Dirichlet non-improvable numbers with certain order in the theory of continued fractions * * This work was supported by NSFC 11571127, 11871208.
Sign Up to like & getrecommendations! Published in 2021 at "Nonlinearity"
DOI: 10.1088/1361-6544/abe097
Abstract: Let [a 1(x), a 2(x), …, a n (x), …] be the continued fraction expansion of x ∈ [0, 1) and q n (x) be the denominator of the nth convergent. The study of relative… read more here.
Keywords: sets dirichlet; certain order; numbers certain; dirichlet non ... See more keywords