Real quadratic function fields of minimal type
type: Item
instance of: scholarly article
zbMATH Open document ID: 1297.11140
DOI: 10.4134/CKMS.2013.28.4.735
author: Dongho Byeon
author: Jiae Keem
author: Sangyoon Lee
published in: Communications of the Korean Mathematical Society
publication date: 2013-12-17T00:00:00Z
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 6239008
zbMATH Keywords: function field
zbMATH Keywords: class number
zbMATH Keywords: continued fraction
MaRDI profile type: Publication
full work available at URL: ckms.2013.28.4.735
OpenAlex ID: W2053732769
title: Real quadratic function fields of minimal type
review text: The authors obtain an analog of a result of \textit{F. Kawamoto} and \textit{K. Tomita} [Osaka J. Math. 46, No. 4, 949--993 (2009; Zbl 1247.11140)], to wit: There are exactly 6 class number one real quadratic function fields \(K = \mathbb F_p(x)(\sqrt{D})\) when all odd prime \(p\) are considered, such that \(D \in \mathbb F_p[x]\) is monic square-free of even degree polynomial satisfying \(\deg D > \deg u_D\), where the fundamental unit of \(K\) is of the form \(t_d + u_D \sqrt{D}\). The proof is by explicit continued fraction manipulations, combined with known class number formulas and tabulated class numbers and regulators.
reviewed by: Thomas A. Schmidt
description: scientific article; zbMATH DE number 6239008