تقرير
Tabulation of cubic function fields via polynomial binary cubic forms
العنوان: | Tabulation of cubic function fields via polynomial binary cubic forms |
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المؤلفون: | Rozenhart, Pieter, Jacobson Jr., Michael, Scheidler, Renate |
سنة النشر: | 2010 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Number Theory, 11Y40, 11R16, 11R58, 11Y60 |
الوصف: | 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 $\mathbb{F}_{q}^*$, up to a given bound $B$ on the degree of $D$. 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 $O(B^4 q^B)$ field operations as $B \rightarrow \infty$. The algorithm, examples and numerical data for $q=5,7,11,13$ are included. Comment: 30 pages, minor typos corrected, extra table entries added, revamped complexity analysis of the algorithm. To appear in Mathematics of Computation |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/1004.4785 |
رقم الأكسشن: | edsarx.1004.4785 |
قاعدة البيانات: | arXiv |
الوصف غير متاح. |