On bounds for fundamental units of real quadratic fields
type: Item
instance of: scholarly article
title: On bounds for fundamental units of real quadratic fields
zbMATH Open document ID: 0801.11045
author: Shin-ichi Katayama
author: Shigeru Katayama
published in: Journal of Number Theory
publication date: 1994-07-04T00:00:00Z
review text: The authors prove a theorem, which has as a consequence the equivalence of the following two conjectures: (1) There exist infinitely many real quadratic fields \(\mathbb{Q} (\sqrt{D})\) with class number 1. (2) For any given \(M>0\), there exists at least one real quadratic field \(\mathbb{Q}( \sqrt{D})\) of class number one such that the fundamental unit \(\varepsilon_ D\) of \(\mathbb{Q} (\sqrt{D})\) satisfies \(\varepsilon_ D > f(M,D)\), where \(f\) is a function satisfying certain conditions.
Mathematics Subject Classification ID: 11R27
Mathematics Subject Classification ID: 11R11
zbMATH DE Number: 584054
zbMATH Keywords: real quadratic fields
zbMATH Keywords: class number one
zbMATH Keywords: fundamental unit
reviewed by: Kenneth S. Williams
MaRDI profile type: Publication
full work available at URL: jnth.1994.1020
OpenAlex ID: W2081357210
DOI: 10.1006/JNTH.1994.1020
Recommended article: Lower bounds for fundamental units of real quadratic fields
Recommended article: The fundamental unit and bounds for class numbers of real quadratic fields
Recommended article: New bounds for the fundamental units and class numbers of real quadratic fields
Recommended article: Q4461871
Recommended article: On fundamental units of real quadratic fields with norm \(+1\)
Recommended article: On the fundamental units and the class numbers of real quadratic fields
Recommended article: Effective lower bounds on large fundamental units of real quadratic fields
Recommended article: On fundamental units of real quadratic fields with norm \(-1\)
Recommended article: On the fundamental unit of real quadratic fields with norm 1
description: scientific article; zbMATH DE number 584054