形式Laurent级数域上交错Oppenheim展开的研究

数学物理学报 ›› 2010, Vol. 30 ›› Issue (1): 207-216.

形式Laurent级数域上交错Oppenheim展开的研究

沈陆明, 张继宏, 镇志勇

1.华中科技大学数学与统计学院武汉 430073|2.湖南农业大学理学院长沙 410128

收稿日期:2007-10-11 修回日期:2009-06-30 出版日期:2010-01-01 发布日期:2010-01-01
基金资助:
湖南农业大学人才引进基金(05YJ06)和湖南省自然科学基金(06JJ2100)资助.

Alternating Oppenheim Expansions over the Field of Formal Laurent Series

SHEN Lu-Ming, ZHANG Ji-Hong, ZHEN Zhi-Yong

1.School of Mathematics and Statistic, Huazhong University of Science and Technology, Wuhan 430073|2.Science College, Hunan Agriculture University, Changsha 410128

Received:2007-10-11 Revised:2009-06-30 Online:2010-01-01 Published:2010-01-01
Supported by:
湖南农业大学人才引进基金(05YJ06)和湖南省自然科学基金(06JJ2100)资助.

摘要/Abstract

摘要：

该文介绍了形式Laurent级数域上交错Oppenheim展开的算法, 得到了该展开中数字的强(弱)大数定理、中心极限定理和重对数率, 并且研究了这些级数部分和的逼近的度.

关键词: 交错Oppenheim展开, 形式Laurent级数, 度量性质, 收敛速度

Abstract:

In this paper, we introduce a new algorithm, alternating Oppenheim expansion over the field of formal Laurent series. Metric properties, such as strong and weak number laws, central limit theorem, and iterated logarithm law, of the digits occurring in this expansion are considered. At the same time, we investigate the approximation orders by rational fractions which are the partial sums of these series.

Key words: Alternating Oppenheim expansion, Formal Laurent series, Metric property, Convergence speed

中图分类号:

11K55

沈陆明, 张继宏, 镇志勇. 形式Laurent级数域上交错Oppenheim展开的研究[J]. 数学物理学报, 2010, 30(1): 207-216.

SHEN Lu-Ming, ZHANG Ji-Hong, ZHEN Zhi-Yong. Alternating Oppenheim Expansions over the Field of Formal Laurent Series[J]. Acta mathematica scientia,Series A, 2010, 30(1): 207-216.

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