Metric properties and exceptional sets of the Oppenheim expansions over the field of Laurent series

被引：4

作者：

Fan, AH ^{[1
]}

Wu, J

机构：

[1] Wuhan Univ, Dept Math, Wuhan 430072, Peoples R China

[2] Univ Picardie, F-80039 Amiens, France

[3] Inst Math Luminy, Amiens, France

[4] LAMFA, CNRS, UMR 6140, Amiens, France

来源：

CONSTRUCTIVE APPROXIMATION | 2004年 / 20卷 / 04期

关键词：

Oppenheim expansions; Laurent series; finite field; Hausdorff dimension;

D O I：

10.1007/s00365-003-0537-2

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We investigate metric properties of the polynomial digits occurring in a large class of Oppenheim expansions of Laurent series, including Luroth, Engel, and Sylvester expansions of Laurent series and Cantor infinite products of Laurent series. The obtained results cover those for special cases of Luroth and Engel expansions obtained by Grabner, A. Knopfmacher, and J. Knopfmacher. Our results applied in the cases of Sylvester expansions and Cantor infinite products are original. We also calculate the Hausdorff dimensions of different exceptional sets on which the above-mentioned metric properties fail to hold.

引用

页码：465 / 495

页数：31

共 28 条

[1] An infinite family of Engel expansions of Rogers-Ramanujan type [J].