A tower with non-Galois steps which attains the Drinfeld-Vladut bound
type: Item
instance of: scholarly article
title: A tower with non-Galois steps which attains the Drinfeld-Vladut bound
zbMATH Open document ID: 1060.11078
author: Juscelino Bezerra
author: Arnaldo Garcia
published in: Journal of Number Theory
publication date: 2004-08-04T00:00:00Z
review text: A tower \(F_1\subseteq F_2\subseteq\ldots\) of algebraic function fields \({F_i}| {\mathbb F_q}\) is said to be asymptotically optimal if \(\text{ lim}_{i\to\infty} F_i(\mathbb F_q)/g_i(F_i)\) is equal to the Drinfeld-Vladut bound \(\sqrt{q}-1\). For \(q\) a square, several of such towers were explicitly constructed by \textit{A. Garcia} and \textit{H. Stichtenoth} [see Invent. Math. 121, 211--222 (1995; Zbl 0822.11078) and J. Number Theory 61, 248--273 (1996; Zbl 0893.11047)]. A property of these towers is that each step \(F_{i+1}| F_i\) is Galois. In this paper, for \(q>4\), the authors construct an asymptotically optimal tower with non-Galois steps.
reviewed by: Fernando Torres
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11T71
zbMATH DE Number: 2081176
zbMATH Keywords: towers of function fields
zbMATH Keywords: finite fields
zbMATH Keywords: rational places
zbMATH Keywords: Drinfeld-Vladut bound
zbMATH Keywords: genus
MaRDI profile type: Publication
full work available at URL: j.jnt.2003.11.004
OpenAlex ID: W1990277861
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DOI: 10.1016/J.JNT.2003.11.004
description: scientific article; zbMATH DE number 2081176