Application of a character sum estimate to a 2-class number density
type: Item
instance of: scholarly article
title: Application of a character sum estimate to a 2-class number density
zbMATH Open document ID: 0551.12002
DOI: 10.1016/0022-314X(84)90108-2
author: Frank III Gerth
author: Sidney W. Graham
published in: Journal of Number Theory
publication date: 1984-01-01T00:00:00Z
review text: Sei \(A_{2,X}\) die Menge aller quadratfreien natürlichen Zahlen \(n\leq x\) derart, daß im imaginär-quadratischen Körper \({\mathbb{Q}}(\sqrt{- n})\) genau zwei Primzahlen verzweigen, und sei \(B_{2,X}\) die Menge aller \(n\in A_{2,X}\), für welche \({\mathbb{Q}}(\sqrt{-n})\) die Klassenzahl 4 hat. Dann gilt mit \(C(x)=(x\quad \log \log x)\cdot (\log x)^{-1}:\) \(| A_{2,X}| =1/2 C(x)+O(x/\log x),\) \(| B_{2,X}| =1/4 C(x)+O(x/\log x).\)
reviewed by: Franz Halter-Koch
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R23
Mathematics Subject Classification ID: 11L40
zbMATH DE Number: 3877302
zbMATH Keywords: character sum estimate
zbMATH Keywords: imaginary quadratic field
zbMATH Keywords: ramification of primes
zbMATH Keywords: class number four
MaRDI profile type: Publication
cites work: Q3900124
cites work: On the averages of some arithmetical functions of two variables
cites work: Q4164380
cites work: Density results for the 2-classgroups of imaginary quadratic fields.
cites work: Arithmetischer Beweis des Satzes über die Anzahl der durch vier teilbaren Invarianten der absoluten Klassengruppe im quadratischen Zahlkörper.
description: scientific article; zbMATH DE number 3877302