On Real Quadratic Fields Containing Units with Norm -1

DOI10.1017/S0027763000012939zbMath0167.04401MaRDI QIDQ5552816

Hideo Yokoi

Publication date: 1968

Published in: Nagoya Mathematical Journal (Search for Journal in Brave)

zbMATH Keywords

class numbersreal quadratic fieldsfundamental units

Mathematics Subject Classification ID

Quadratic extensions (11R11) Units and factorization (11R27) Class numbers, class groups, discriminants (11R29)

Related Items (23)

SIC-POVMs from Stark units: Prime dimensions n2 + 3 ⋮ On the Insolubility of a Class of Diophantine Equations and the Nontriviality of the Class Numbers of Related Real Quadratic Fields of Richaud-Degert Type ⋮ New invariants and class number problem in real quadratic fields ⋮ Class numbers of certain families of totally real biquadratic fields and a result of Mollin ⋮ Unit reducible fields and perfect unary forms ⋮ GENERALIZED WALL-SUN-SUN PRIMES AND MONOGENIC POWER-COMPOSITIONAL TRINOMIALS ⋮ A new condition for \(k\)-Wall-Sun-Sun primes ⋮ Fields of small class number in the family \(\mathbb{Q}(\sqrt{9m^2+4m})\) ⋮ On fundamental units of real quadratic fields with norm \(-1\) ⋮ A note on the class-number of real quadratic fields with prime discriminants ⋮ On fundamental units of real quadratic fields with norm \(+1\) ⋮ Lower bound for the class number of \(\mathbb{Q} (\sqrt{n^2+4})\) ⋮ Lower Bounds for Class Numbers of Real Quadratic Fields ⋮ On the Sylow \(p\)-subgroups of the ideal class groups of some imaginary cyclic fields of degree \(p-1\) ⋮ The fundamental unit and bounds for class numbers of real quadratic fields ⋮ Lower Bounds for Class Numbers of Real Quadratic and Biquadratic Fields ⋮ ON NUMBER FIELDS WITHOUT A UNIT PRIMITIVE ELEMENT ⋮ On the divisor function and class numbers of real quadratic fields. I ⋮ On the fundamental unit of real quadratic fields with norm 1 ⋮ On the divisor function and class numbers of real quadratic fields. II ⋮ Class number two problem for real quadratic fields with fundamental units with the positive norm ⋮ A necessary and sufficient condition for \(k=\mathbb{Q}\left ( \sqrt{4 n^2 + 1}\right)\) to have class number \(\omega\left( n\right)+c \) ⋮ Lower bound for class numbers of certain real quadratic fields

Cites Work

• Über die Bestimmung der Grundeinheit gewisser reell-quadratischer Zahlkörper
• Unnamed Item

This page was built for publication: On Real Quadratic Fields Containing Units with Norm -1