Tabulation of Cubic Function Fields Via Polynomial Binary Cubic Forms
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | Department of Mathematics and Statistics | |
| dc.contributor.author | ROZENHART, Pieter | |
| hal.structure.identifier | Department of Computer Science [Calgary] [CPSC] | |
| dc.contributor.author | JACOBSON JR., Michael | |
| hal.structure.identifier | Department of Mathematics and Statistics | |
| dc.contributor.author | SCHEIDLER, Renate | |
| dc.date.accessioned | 2024-04-04T02:29:06Z | |
| dc.date.available | 2024-04-04T02:29:06Z | |
| dc.date.created | 2010-04-27 | |
| dc.date.issued | 2012 | |
| dc.identifier.issn | 0025-5718 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190147 | |
| dc.description.abstractEn | We present a method for tabulating all cubic function fields over $\mathbb{F}_{q}(t)$ whose discriminant $D$ has either odd degree or even degree and the leading coefficient of $-3D$ is a non-square in $\mathbb_{q}^*$, up to a given bound $X$ on $|D| = q^{\deg(D)}$. Our method is based on a generalization of Belabas' method for tabulating cubic number fields. The main theoretical ingredient is a generalization of a theorem of Davenport and Heilbronn to cubic function fields, along with a reduction theory for binary cubic forms that provides an efficient way to compute equivalence classes of binary cubic forms. The algorithm requires $O(q^4 X^{1+\epsilon})$ field operations when $D$ has odd degree, and $O(q^5 X^{1+\epsilon})$ when $D$ has even degree. It performs quite well in practice. The algorithm, examples and numerical data for $q=5,7,11,13$ are included. | |
| dc.language.iso | en | |
| dc.publisher | American Mathematical Society | |
| dc.title.en | Tabulation of Cubic Function Fields Via Polynomial Binary Cubic Forms | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1090/S0025-5718-2012-02591-9 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1004.4785 | |
| bordeaux.journal | Mathematics of Computation | |
| bordeaux.page | 2335-2359 | |
| bordeaux.volume | 81 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 280 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00477111 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00477111v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Mathematics%20of%20Computation&rft.date=2012&rft.volume=81&rft.issue=280&rft.spage=2335-2359&rft.epage=2335-2359&rft.eissn=0025-5718&rft.issn=0025-5718&rft.au=ROZENHART,%20Pieter&JACOBSON%20JR.,%20Michael&SCHEIDLER,%20Renate&rft.genre=article |
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