A positive density of fundamental discriminants with large regulator
type: Item
instance of: scholarly article
title: A positive density of fundamental discriminants with large regulator
zbMATH Open document ID: 1307.11037
author: Florent Jouve
author: Étienne Fouvry
published in: Pacific Journal of Mathematics
publication date: 2013-06-19T00:00:00Z
review text: Let \(\varepsilon_D\) be the fundamental unit of a quadratic number field of discriminant \(D\). The authors prove under some mild technical restrictions that \[ \sharp \{D\leq X : \varepsilon_D\geq D^{3-\delta}\}\gg_\delta X \] for any \(\delta>0\), provided the norm of \(\varepsilon_D\) is positive. Moreover, they show that there exists a constant \(\delta>0\) such that \[ \sum_{D\leq x;\; 4\| D}h(D)\leq \left(\frac{8}{21 \pi^2}C_0-\delta\right) \frac{x^{3/2}}{\log x}, \] where \(C_0\) is defined by a converging Euler product.
reviewed by: Volker Ziegler
Mathematics Subject Classification ID: 11D09
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 6177098
zbMATH Keywords: regulator of a real quadratic field
zbMATH Keywords: Pell equation
MaRDI profile type: Publication
full work available at URL: pjm.2013.262.81
OpenAlex ID: W2109600617
DOI: 10.2140/PJM.2013.262.81
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description: scientific article; zbMATH DE number 6177098