ROZENHART, Pieter; JACOBSON JR., Michael; SCHEIDLER, Renate

doi:10.1216/RMJ-2015-45-6-1985

Métadonnées

Afficher la notice complète

Licence d’utilisation du document

ROZENHART, Pieter
Lithe and fast algorithmic number theory [LFANT]
University of Calgary

JACOBSON JR., Michael
University of Calgary

SCHEIDLER, Renate
University of Calgary

Langue

Article de revue

Ce document a été publié dans

Rocky Mountain Journal of Mathematics. 2015, vol. 45, n° 6, p. 1985-2022

Rocky Mountain Mathematics Consortium

Résumé en anglais

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.< Réduire

Métadonnées

Partager cette publication !

Licence d’utilisation du document

Computing quadratic function fields with high 3-rank via cubic field tabulation

Langue

Ce document a été publié dans

Résumé en anglais

URI

DOI

Origine

Unités de recherche