Metrical properties for continued fractions of formal Laurent series

Hu, Hui; Hussain, Mumtaz; Yu, Yueli

doi:10.1016/j.ffa.2021.101850

Cited by 5 publications

(1 citation statement)

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“…Based on the main results in Wang and Wu [33], Fang, Ma and Song [10] recently obtained the Hausdorff dimensions of some exceptional sets of Borel-Bernstein theorem. Also, questions in the same flavor for continued fractions of Laurent series have been studied by Hu, Wang, Wu and Yu [19], Hu, Hussain and Yu [18]. Motivated by the characterizations related to these two sets in regular continued fraction and continued fractions over the field of formal Laurent series, we will pay attention to the metric results in the setting of Schneider's p-adic continued fraction.…”

Section: Introductionmentioning

confidence: 99%

A Study of the Writing Features of Primary School Mathematics Textbooks

Song

Yun-ming

Qiu

et al. 2021

School Mathematics Textbooks in China

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Let Z p be the ring of p-adic integers and a n pxq be the n-th digit of Schneider's p-adic continued fraction of x P pZ p . We study the growth rate of the digits ta n pxqu ně1 from the viewpoint of multifractal analysis. The Hausdorff dimension of the set) is completely determined for any ψ : N Ñ R `satisfying ψpnq Ñ 8 as n Ñ 8. As an application, we also calculate the Hausdorff dimension of the intersection setsfor the above function ψ and 0 ď α 1 ă α 2 ď 8.

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