Binary forms and orders of algebraic number fields
type: Item
instance of: scholarly article
title: Binary forms and orders of algebraic number fields
zbMATH Open document ID: 0647.10018
DOI: 10.1007/BF01389040
author: Jin Nakagawa
published in: Inventiones Mathematicae
publication date: 1989-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/143700
review text: We define a mapping of the space of binary forms of degree \(n>3\) to the space of quadratic forms of n-1 variables. Using the mapping, we obtain a lower estimate for a certain sum of class numbers of totally real binary forms of degree \(n>3\). At the same time, we obtain a lower estimate for the number of orders of totally real algebraic number fields of degree \(n>3\). Further, we prove that there exist infinitely many real quadratic fields having an \(A_ n\)-extension which is unramified at all primes including the infinite primes.
Mathematics Subject Classification ID: 11E76
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 11R80
zbMATH DE Number: 4055711
zbMATH Keywords: lower estimate
zbMATH Keywords: sum of class numbers
zbMATH Keywords: totally real binary forms
zbMATH Keywords: orders
zbMATH Keywords: totally real algebraic number fields
zbMATH Keywords: binary form of higher degree
zbMATH Keywords: unramified Galois extension
MaRDI profile type: Publication
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OpenAlex ID: W4233168156
description: scientific article; zbMATH DE number 4055711