Class number 2 criteria for real quadratic fields of Richaud-Degert type

DOI10.1006/jnth.1997.2059zbMath0871.11076OpenAlexW1977687211MaRDI QIDQ676211

Hyun Kwang Kim, Dongho Byeon

Publication date: 16 March 1997

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jnth.1997.2059

zbMATH Keywords

real quadratic fieldsRichaud-Degert typeclass number two criteria

Mathematics Subject Classification ID

Quadratic extensions (11R11) Class numbers, class groups, discriminants (11R29)

Related Items (15)

Class numbers of certain families of totally real biquadratic fields and a result of Mollin ⋮ Polynomial behavior of special values of partial zeta functions of real quadratic fields at \(s = 0\) ⋮ Fields of small class number in the family \(\mathbb{Q}(\sqrt{9m^2+4m})\) ⋮ A NOTE ON CERTAIN REAL QUADRATIC FIELDS WITH CLASS NUMBER UP TO THREE ⋮ Unnamed Item ⋮ Some criteria for class numbers to be non-one ⋮ Partial Dedekind Zeta Values and Class Numbers of R–D Type Real Quadratic Fields ⋮ Lower bound for the class number of \(\mathbb{Q} (\sqrt{n^2+4})\) ⋮ Class number 2 problem for certain real quadratic fields of Richaud-Degert type ⋮ Caliber number of real quadratic fields ⋮ On the structure of order 4 class groups of \(\mathbb{Q}(\sqrt{n^2+1})\) ⋮ Evaluation of the Dedekind zeta functions at \(s=-1\) of the simplest quartic fields ⋮ The complete determination of narrow Richaud-Degert type which is not 5 modulo 8 with class number two ⋮ 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

• Unnamed Item
• On a determination of certain real quadratic fields of class number two
• Über die Bestimmung der Grundeinheit gewisser reell-quadratischer Zahlkörper
• On the values at negative integers of the zeta-function of a real quadratic field
• Real quadratic fields with class numbers divisible by \(n\)
• Class number 1 criteria for real quadratic fields of Richaud-Degert type
• On unramified Galois extensions of quadratic number fields
• Generalized Dedekind sums and transformation formulae of certain Lambert series
• Some theorems on generalized Dedekind sums
• Über eine Gattung elementar-arithmetischer Klasseninvarianten reell-quadratischer Zahlkörper.

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