On the construction of continued fraction normal series in positive characteristic

Dong Han Kim; Hitoshi Nakada; Rie Natsui

doi:10.3836/tjm/1475723093

On the construction of continued fraction normal series in positive characteristic

Dong Han Kim, Hitoshi Nakada, Rie Natsui

Department of Mathematics Education

Research output: Contribution to journal › Article › peer-review

Abstract

Motivated by the famous Champernowne construction of a normal number, R. Adler, M. Keane, and M. Smorodinsky constructed a normal number with respect to the simple continued fraction transformation. In this paper, we follow their idea and construct a normal series for the Artin continued fraction expansion in positive characteristic. A normal series for Lüroth expansion is also discussed.

Original language	English
Pages (from-to)	679-694
Number of pages	16
Journal	Tokyo Journal of Mathematics
Volume	39
Issue number	3
DOIs	https://doi.org/10.3836/tjm/1475723093
State	Published - Mar 2017

Keywords

Continued fractions
Normal numbers

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10.3836/tjm/1475723093

Cite this

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title = "On the construction of continued fraction normal series in positive characteristic",

abstract = "Motivated by the famous Champernowne construction of a normal number, R. Adler, M. Keane, and M. Smorodinsky constructed a normal number with respect to the simple continued fraction transformation. In this paper, we follow their idea and construct a normal series for the Artin continued fraction expansion in positive characteristic. A normal series for L{\"u}roth expansion is also discussed.",

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AU - Nakada, Hitoshi

AU - Natsui, Rie

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AB - Motivated by the famous Champernowne construction of a normal number, R. Adler, M. Keane, and M. Smorodinsky constructed a normal number with respect to the simple continued fraction transformation. In this paper, we follow their idea and construct a normal series for the Artin continued fraction expansion in positive characteristic. A normal series for Lüroth expansion is also discussed.

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KW - Normal numbers

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On the construction of continued fraction normal series in positive characteristic

Abstract

Keywords

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