Residuacity properties of real quadratic units
type: Item
instance of: scholarly article
title: Residuacity properties of real quadratic units
zbMATH Open document ID: 0272.12002
DOI: 10.1016/0022-314X(73)90071-1
author: Jacob A. Brandler
published in: Journal of Number Theory
publication date: 1973-01-01T00:00:00Z
review text: The main result of the present paper is that if \(m = 5\) or \(13\), and if \(p\) is a rational prime such that \((-1/p) = 1 = (m/p)\), then \([\varepsilon_m/\mathfrak p] = 1\) if and only if \(p=x^2 + 4my^2\) \((x\in \mathbb Z,\ y\in\mathbb Z)\), where \(\varepsilon_m\) denotes the fundamental unit of the field \(K=\mathbb Q(m^{1/2})\) and \([\cdot / \cdot]\) denotes the Legendre symbol of the ring of integers of \(K\) with \(\mathfrak p\) a prime ideal divisor of \(p\) in \(K\).
reviewed by: Oleg M. Fomenko
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11A41
zbMATH DE Number: 3427485
zbMATH Keywords: necessary and sufficient conditions for representing certain classes of primes by given quadratic forms
zbMATH Keywords: techniques of rational number theory
MaRDI profile type: Publication
cites work: Note on primes of type x2 + 32y2, class number, and residuacity.
cites work: Q5610449
full work available at URL: 0022-314x(73)90071-1
OpenAlex ID: W2069194104
description: scientific article; zbMATH DE number 3427485