Tokyo Journal of Mathematics

On the Construction of Continued Fraction Normal Series in Positive Characteristic

Dong Han KIM, Hitoshi NAKADA, and Rie NATSUI

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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\"uroth expansion is also discussed.

Article information

Source
Tokyo J. of Math., Volume 39, Number 3 (2017), 679-694.

Dates
First available in Project Euclid: 6 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.tjm/1475723093

Digital Object Identifier
doi:10.3836/tjm/1475723093

Mathematical Reviews number (MathSciNet)
MR3634288

Zentralblatt MATH identifier
06727281

Subjects
Primary: 11K16: Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. [See also 11A63]
Secondary: 11J70: Continued fractions and generalizations [See also 11A55, 11K50]

Citation

KIM, Dong Han; NAKADA, Hitoshi; NATSUI, Rie. On the Construction of Continued Fraction Normal Series in Positive Characteristic. Tokyo J. of Math. 39 (2017), no. 3, 679--694. doi:10.3836/tjm/1475723093. https://projecteuclid.org/euclid.tjm/1475723093


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References

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