On the continued fraction expansion of the unique root in $\mathbb{F}_p$ of the equation $x^4+x^2-Tx-1/12=0$ and other related hyperquadratic expansions
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LASJAUNIAS, Alain | |
| dc.date.accessioned | 2024-04-04T02:28:42Z | |
| dc.date.available | 2024-04-04T02:28:42Z | |
| dc.date.created | 2010-09-30 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 1071-5797 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190116 | |
| dc.description.abstractEn | 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. | |
| dc.language.iso | en | |
| dc.publisher | Elsevier | |
| dc.subject.en | Continued fractions | |
| dc.subject.en | Fields of power series | |
| dc.subject.en | Finite fields. | |
| dc.subject.en | Finite fields | |
| dc.title.en | On the continued fraction expansion of the unique root in $\mathbb{F}_p$ of the equation $x^4+x^2-Tx-1/12=0$ and other related hyperquadratic expansions | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1016/j.ffa.2011.06.001 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1009.6139 | |
| bordeaux.journal | Finite Fields and Their Applications | |
| bordeaux.page | 26-34 | |
| bordeaux.volume | 18 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 1 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | hal-00524551 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-00524551v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Finite%20Fields%20and%20Their%20Applications&rft.date=2012&rft.volume=18&rft.issue=1&rft.spage=26-34&rft.epage=26-34&rft.eissn=1071-5797&rft.issn=1071-5797&rft.au=LASJAUNIAS,%20Alain&rft.genre=article |
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