Class number 1 criteria for real quadratic fields of Richaud-Degert type

DOI10.1006/jnth.1996.0052zbMath0846.11060OpenAlexW2983437486MaRDI QIDQ1912294

Hyun Kwang Kim, Dongho Byeon

Publication date: 26 September 1996

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

Full work available at URL: https://doi.org/10.1006/jnth.1996.0052

zbMATH Keywords

class number oneSiegel's formulareal quadratic fields of Richaud-Degert typespecial values of the zeta function

Mathematics Subject Classification ID

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

Related Items (16)

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 ⋮ Unnamed Item ⋮ Class number one problem for the real quadratic fields \(\mathbb{Q}(\sqrt{m^2+2r})\) ⋮ Some criteria for class numbers to be non-one ⋮ Partial Dedekind Zeta Values and Class Numbers of R–D Type Real Quadratic Fields ⋮ Class number 2 criteria for real quadratic fields of Richaud-Degert type ⋮ Lower bound for the class number of \(\mathbb{Q} (\sqrt{n^2+4})\) ⋮ A complete determination of Rabinowitsch polynomials ⋮ 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 ⋮ 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

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