Taiwanese Journal of Mathematics

CUBIC FORMAL POWER SERIES IN CHARACTERISTIC 2 WITH UNBOUNDED PARTIAL QUOTIENTS

K. Ayadi, M. Hbaib, and F. Mahjoub

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Abstract

There is a theory of continued fractions for formal power series in $x^{−1}$ with coefficients in a field $\mathbb{F}_q$. This theory bears a close analogy with classical continued fractions for real numbers with formal power series playing the role of real numbers and the sum of the terms of non-negative degree in $x$ playing the role of the integral part. We give a family of cubic power series over $\mathbb{F}_2$ with unbounded partial quotients. To be more precise, let $f \in \mathbb{F}_2((x^{−1}))$ such that $f$ is not polynomial but $f^3$ is polynomial with degreed $d \in 3\mathbb{N}$, we prove that the continued fraction expansion of $f$ is unbounded.

Article information

Source
Taiwanese J. Math., Volume 15, Number 5 (2011), 2331-2336.

Dates
First available in Project Euclid: 18 July 2017

Permanent link to this document
https://projecteuclid.org/euclid.twjm/1500406437

Digital Object Identifier
doi:10.11650/twjm/1500406437

Mathematical Reviews number (MathSciNet)
MR2880407

Zentralblatt MATH identifier
1253.11074

Subjects
Primary: 11A55: Continued fractions {For approximation results, see 11J70} [See also 11K50, 30B70, 40A15] 11R58: Arithmetic theory of algebraic function fields [See also 14-XX]

Keywords
finite fields formal power series continued fraction

Citation

Ayadi, K.; Hbaib, M.; Mahjoub, F. CUBIC FORMAL POWER SERIES IN CHARACTERISTIC 2 WITH UNBOUNDED PARTIAL QUOTIENTS. Taiwanese J. Math. 15 (2011), no. 5, 2331--2336. doi:10.11650/twjm/1500406437. https://projecteuclid.org/euclid.twjm/1500406437


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References

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