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| HAL: hal-00524551, version 1 |
| arXiv: 1009.6139 |
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| On the continued fraction expansion of the unique root in F(p) of the equation x^4+x^2-Tx-1:12=0 and other related hyperquadratic expansions |
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| Alain Lasjaunias 1 |
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| (2010-09-30) |
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| In 1985, Robbins observed by computer the continued fraction expansion of certain algebraic power series over a finite field. Incidentally, he came across a particular equation of degree 4 in characteristic p=13. This equation has an analogue for all primes p>=5. There are two patterns for the continued fraction of the solution of this equation, according to the residue of p modulo 3. We describe this pattern in the first case, considering especially p=7 and p=13. in the second case we only give indications. |
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| 1: | Institut de Mathématiques de Bordeaux (IMB) |
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CNRS : UMR5251 – Université Sciences et Technologies - Bordeaux I – Université Victor Segalen - Bordeaux II |
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| Subject | : | Mathematics/Number Theory |
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| Continued fractions – Fields of power series – Finite fields. |
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| Fulltext link: |
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| http://fr.arXiv.org/abs/1009.6139 |
| hal-00524551, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00524551 | |
| oai:hal.archives-ouvertes.fr:hal-00524551 | |
| From: Alain Lasjaunias | |
| Submitted on: Friday, 8 October 2010 10:33:35 | |
| Updated on: Friday, 8 October 2010 10:33:35 | |
