Computing quadratic function fields with high 3-rank via cubic field tabulation
| hal.structure.identifier | Lithe and fast algorithmic number theory [LFANT] | |
| hal.structure.identifier | University of Calgary | |
| dc.contributor.author | ROZENHART, Pieter | |
| hal.structure.identifier | University of Calgary | |
| dc.contributor.author | JACOBSON JR., Michael | |
| hal.structure.identifier | University of Calgary | |
| dc.contributor.author | SCHEIDLER, Renate | |
| dc.date.accessioned | 2024-04-04T02:29:20Z | |
| dc.date.available | 2024-04-04T02:29:20Z | |
| dc.date.created | 2010 | |
| dc.date.issued | 2015 | |
| dc.identifier.issn | 0035-7596 | |
| dc.identifier.uri | https://oskar-bordeaux.fr/handle/20.500.12278/190166 | |
| dc.description.abstractEn | We present recent results on the computation of quadratic function fields with high 3-rank. Using a generalization of a method of Belabas on cubic field tabulation and a theorem of Hasse, we compute quadratic function fields with 3-rank $ \geq 1$, of imaginary or unusual discriminant $D$, for a fixed $|D| = q^{\deg(D)}$. We present numerical data for quadratic function fields over $\mathbb{F}_{5}, \mathbb{F}_{7}, \mathbb{F}_{11}$ and $\mathbb{F}_{13}$ with $\deg(D) \leq 11$. Our algorithm produces quadratic function fields of minimal genus for any given 3-rank. Our numerical data mostly agrees with the Friedman-Washington heuristics for quadratic function fields over the finite field $\mathbb{F}_{q}$ where $q \equiv -1 \pmod{3}$. The data for quadratic function fields over the finite field $\mathbb{F}_{q}$ where $q \equiv 1 \pmod{3}$ does not agree closely with Friedman-Washington, but does agree more closely with some recent conjectures of Malle. | |
| dc.language.iso | en | |
| dc.publisher | Rocky Mountain Mathematics Consortium | |
| dc.title.en | Computing quadratic function fields with high 3-rank via cubic field tabulation | |
| dc.type | Article de revue | |
| dc.identifier.doi | 10.1216/RMJ-2015-45-6-1985 | |
| dc.subject.hal | Mathématiques [math]/Théorie des nombres [math.NT] | |
| dc.identifier.arxiv | 1003.1287 | |
| bordeaux.journal | Rocky Mountain Journal of Mathematics | |
| bordeaux.page | 1985-2022 | |
| bordeaux.volume | 45 | |
| bordeaux.hal.laboratories | Institut de Mathématiques de Bordeaux (IMB) - UMR 5251 | * |
| bordeaux.issue | 6 | |
| bordeaux.institution | Université de Bordeaux | |
| bordeaux.institution | Bordeaux INP | |
| bordeaux.institution | CNRS | |
| bordeaux.peerReviewed | oui | |
| hal.identifier | inria-00462008 | |
| hal.version | 1 | |
| hal.popular | non | |
| hal.audience | Internationale | |
| hal.origin.link | https://hal.archives-ouvertes.fr//inria-00462008v1 | |
| bordeaux.COinS | ctx_ver=Z39.88-2004&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.jtitle=Rocky%20Mountain%20Journal%20of%20Mathematics&rft.date=2015&rft.volume=45&rft.issue=6&rft.spage=1985-2022&rft.epage=1985-2022&rft.eissn=0035-7596&rft.issn=0035-7596&rft.au=ROZENHART,%20Pieter&JACOBSON%20JR.,%20Michael&SCHEIDLER,%20Renate&rft.genre=article |
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