Cyclotomic function fields with divisor class number one
type: Item
instance of: scholarly article
title: Cyclotomic function fields with divisor class number one
zbMATH Open document ID: 0734.11060
author: Masanari Kida
author: Naoki Murabayashi
published in: Tokyo Journal of Mathematics
publication date: 1991-01-01T00:00:00Z
review text: Let \(k\) denote the rational function field over any finite field \(F\). For any non-constant polynomial \(M\) over \(F\), the authors define the cyclotomic function field \(K_ M\), an extension of \(k\), after \textit{S. Galovich} and \textit{M. Rosen} [J. Number Theory 13, 363--375 (1981; Zbl 0473.12014)]. They obtain formulae for the genera of \(K_ M\) and of its ``maximal real subfield'' \(K_ M^+\) and apply them to determine all fields \(K_ M\) and \(K_ M^+\) with class number one. A complete list of the fields \(K_ M\) and \(K_ M^+\) with genus one is also given.
Mathematics Subject Classification ID: 11R29
Mathematics Subject Classification ID: 11R18
Mathematics Subject Classification ID: 11R58
zbMATH DE Number: 4214148
zbMATH Keywords: cyclotomic function field
zbMATH Keywords: class number one
zbMATH Keywords: genus one
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.3836/tjm/1270130486
OpenAlex ID: W1975452553
DOI: 10.3836/TJM/1270130486
description: scientific article; zbMATH DE number 4214148