On the density of cyclic quartic fields
type: Item
instance of: scholarly article
zbMATH Open document ID: 0996.11068
DOI: 10.4153/CMB-2001-012-6
author: Zhiming M. Ou
author: Kenneth S. Williams
published in: Canadian Mathematical Bulletin
publication date: 2002-11-04T00:00:00Z
Mathematics Subject Classification ID: 11R16
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 1643717
zbMATH Keywords: density
zbMATH Keywords: cyclic quartic fields
zbMATH Keywords: discriminant
MaRDI profile type: Publication
title: On the density of cyclic quartic fields
review text: Let \(h(n)\) denote the number of cyclic quartic fields over the rational number field \(Q\) with discriminant \(n\) and set \(N(x)= \sum_{n\leq x}h(n)\). Then, \textit{A. M. Baily} provided an asymptotic formula for \(N(X)\) [cf. J. Reine Angew. Math. 315, 190-210 (1980; Zbl 0421.12007)]. However, his generating function \(f(s)= \sum_{n=1}^\infty \frac{h(n)}{n^s}\) is given incorrectly. In this paper, using the representation of a cyclic quartic field given by one of the authors and others and an elementary method, they correct Baily's result.
reviewed by: Hideo Yokoi
description: scientific article; zbMATH DE number 1643717