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- W2989769567 abstract "In this article we aim to investigate the Hausdorff dimension of the set of points $x in [0,1)$ such that for any $rinmathbb{N},$ begin{align*} a_{n+1}(x)a_{n+2}(x)cdots a_{n+r}(x)geq e^{tau(x)(h(x)+cdots+h(T^{n-1}(x)))} {align*} holds for infinitely many $ninmathbb{N},$ where $h$ and $tau$ are positive continuous functions, $T$ is the Gauss map and $a_n(x)$ denote the $n$th partial quotient of $x$ in its continued fraction expansion. By appropriate choices of $r$, $tau(x)$ snd $h(x)$ we obtain the classical Jarnik-Besicovitch Theorem as well as more recent results by Wang-Wu-Xu, Wang-Wu, Huang-Wu-Xu and Hussain-Kleinbock-Wadleigh-Wang." @default.
- W2989769567 created "2019-12-05" @default.
- W2989769567 creator A5063614880 @default.
- W2989769567 date "2019-11-28" @default.
- W2989769567 modified "2023-09-27" @default.
- W2989769567 title "Hausdorff dimension for the set of points connected with the generalized Jarn'ik-Besicovitch set" @default.
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