A problem on quadratic fields
type: Item
instance of: scholarly article
title: A problem on quadratic fields
zbMATH Open document ID: 0662.12004
author: Takashi Ono
published in: Proceedings of the Japan Academy. Series A
publication date: 1988-01-01T00:00:00Z
review text: For a quadratic field \(k\), let \(M_ k\) denote the Minkowski constant and \(\chi_ k\) the Kronecker character of \(k\). The author considers explicit determination of the sets \(K^ 0\), \(K^{-}\) and \(K^{+}\) consisting of those \(k\) for which all rational primes \(p\leq M_ k\) satisfy \(\chi_ k(p)=0, -1\) or \(+1\), respectively. He determines \(K^ 0\) in a simple way and offers for \(K^{-}\) a list of \(k\) which is complete up to one possible additional field (which he conjectures does not exist). In fact, \(K^{-}\) is related to the class number one problem. The set \(K^{+}\), related to the problem of the least quadratic nonresidue, is given conjecturally. [See also \textit{M. Leu}, Proc. Japan Acad., Ser. A 63, 323--326 (1987; Zbl 0659.12004) and Nagoya Math. J. 115, 185--198 (1989; Zbl 0659.12005).]
Mathematics Subject Classification ID: 11R11
Mathematics Subject Classification ID: 11R29
zbMATH DE Number: 4081679
zbMATH Keywords: quadratic field
zbMATH Keywords: Minkowski constant
zbMATH Keywords: Kronecker character
zbMATH Keywords: class number one problem
zbMATH Keywords: least quadratic nonresidue
MaRDI profile type: Publication
full work available at URL: pjaa.64.78
OpenAlex ID: W2052183352
cites work: On two conjectures on real quadratic fields
cites work: On a conjecture of Ono on real quadratic fields
cites work: A complete determination of the complex quadratic fields of class-number one
DOI: 10.3792/PJAA.64.78
description: scientific article; zbMATH DE number 4081679