Metrical properties for continued fractions of formal Laurent series

被引：4

作者：

Hu, Hui ^{[1
,2
]}

Hussain, Mumtaz ^{[2
]}

Yu, Yueli ^{[3
]}

机构：

[1] Nanchang Hangkong Univ, Sch Math & Informat Sci, Nanchang 330063, Jiangxi, Peoples R China

[2] La Trobe Univ, Dept Math & Stat, Bendigo 3552, Australia

[3] Wuhan Univ, Sch Math & Stat, Wuhan 430072, Hubei, Peoples R China

来源：

FINITE FIELDS AND THEIR APPLICATIONS | 2021年 / 73卷

基金：

中国国家自然科学基金; 澳大利亚研究理事会;

关键词：

Formal Laurent series; Continued fraction; Haar measure; Hausdorff dimension; INHOMOGENEOUS DIOPHANTINE APPROXIMATION; HAUSDORFF DIMENSION; PARTIAL QUOTIENTS; FIELD; SETS;

D O I：

10.1016/j.ffa.2021.101850

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Motivated by recent developments in the metrical theory of continued fractions for real numbers concerning the growth of consecutive partial quotients, we consider its analogue over the field of formal Laurent series. Let A(n)(x) be the n th partial quotient of the continued fraction expansion of x in the field of formal Laurent series. We consider the sets of x such that deg A(n+1)(x) + . . . + degA(n+k) (x) >= Phi(n) holds for infinitely many n and for all n respectively, where k >= 1 is an integer and Phi(n) is a positive function defined on N. We determine the size of these sets in terms of Haar measure and Hausdorff dimension. (C) 2021 Elsevier Inc. All rights reserved.

引用

页数：34