On a quartic equation and two families of hyperquadratic continued fractions in pwer series fields
| hal.structure.identifier | Institut de Mathématiques de Bordeaux [IMB] | |
| dc.contributor.author | LASJAUNIAS, Alain | |
| dc.contributor.author | KHALIL, Ayadi | |
| dc.date.accessioned | 2024-04-04T03:19:20Z | |
| dc.date.available | 2024-04-04T03:19:20Z | |
| dc.date.created | 2014-11 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/194495 | |
| dc.description.abstractEn | Casually introduced thirty years ago, a simple algebraic equation of degree 4 with coefficients in F_p[T] has a solution in the field of power series over the finite field F_p. For each p>3, the continued fraction expansion of this solution is remarkable and it has a different general pattern according to the remainder, 1 or 2, in the division of p by 3. We describe two very large families of algebraic continued fractions, each containing these solutions, according to the class of p modulo 3. We compute the irrationality measure for these algebraic continued fractions, and as a consequence, we obtain two different values for the solution of the quartic equation, only depending on the class of p modulo 3. | |
| dc.language.iso | en | |
| dc.subject.en | Continued fractions | |
| dc.subject.en | Fields of power series | |
| dc.subject.en | Finite fields. | |
| dc.title.en | On a quartic equation and two families of hyperquadratic continued fractions in pwer series fields | |
| dc.type | Document de travail - Pré-publication | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1412.0388 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| hal.identifier | hal-01108104 | |
| hal.version | 1 | |
| hal.origin.link | https://hal.archives-ouvertes.fr//hal-01108104v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.au=LASJAUNIAS,%20Alain&KHALIL,%20Ayadi&rft.genre=preprint |
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