The fundamental unit and bounds for class numbers of real quadratic fields

DOI10.1017/S0027763000003834zbMath0728.11050MaRDI QIDQ3351466

Hideo Yokoi

Publication date: 1991

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

zbMATH Keywords

Artin's conjecturereal quadratic fieldsfundamental unitclass number one problembounds for the class numberD- invariantsp-invariant

Mathematics Subject Classification ID

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

Related Items (14)

A note on class number one problem for real quadratic fields ⋮ Fundamental units for real quadratic fields determined by continued fraction conditions ⋮ Lower bounds for fundamental units of real quadratic fields ⋮ Explicit representation of fundamental units of some quadratic fields ⋮ Explicit representation of fundamental units of some real quadratic fields. II ⋮ New invariants and class number problem in real quadratic fields ⋮ On Yokoi’s Invariants and the Ankeny–Artin–Chowla conjecture ⋮ Solvability of the diophantine equation x² − Dy² = ± 2 and new invariants for real quadratic fields ⋮ A handy technique for fundamental unit in specific type of real quadratic fields ⋮ New bounds for the fundamental units and class numbers of real quadratic fields ⋮ A note on the class-number of real quadratic fields with prime discriminants ⋮ Continued fractions and certain real quadratic fields of minimal type ⋮ Ankeny-Artin-Chowla conjecture and continued fraction expansion ⋮ A new condition equivalent to the Ankeny-Artin-Chowla conjecture

Cites Work

• Unnamed Item
• Quadratische Ordnungen mit großer Klassenzahl. (Quadratic orders with large class number)
• Solution of a problem of Yokoi
• On two conjectures on real quadratic fields
• Continued fractions and real quadratic fields
• A complete determination of the complex quadratic fields of class-number one
• The class-number of real quadratic number fields
• The fundamental unit and class number one problem of real quadratic fields with prime discriminant
• On the diophantine equationx²−py²= ± 4qand the class number of real subfields of a cyclotomic field
• Linear forms in the logarithms of algebraic numbers
• On Real Quadratic Fields Containing Units with Norm -1
• On the least solution of Pell’s equation

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