Acta mathematica scientia,Series A ›› 2010, Vol. 30 ›› Issue (1): 207-216.

• Articles • Previous Articles     Next Articles

Alternating Oppenheim Expansions over the Field of Formal Laurent Series

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

  1. 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.

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

CLC Number: 

  • 11K55
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