Fundamental units of real quadratic fields of odd class number

DOI10.1016/J.JNT.2013.10.019zbMath1310.11110OpenAlexW2011491319WikidataQ114157550 ScholiaQ114157550MaRDI QIDQ2637452

Qin Yue, Zhe Zhang

Publication date: 11 February 2014

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

Full work available at URL: https://doi.org/10.1016/j.jnt.2013.10.019

zbMATH Keywords

real quadratic fieldsfundamental unitsDiophantine equationsFermat-Pell equations

Mathematics Subject Classification ID

Units and factorization (11R27) Quadratic and bilinear Diophantine equations (11D09)

Related Items (13)

Congruence relations for the fundamental unit of a pure cubic field and its class number ⋮ Fundamental units for real quadratic fields determined by continued fraction conditions ⋮ Hilbert genus fields of imaginary biquadratic fields ⋮ The 2-rank of the real pure quartic number field \(K= \mathbb{Q}(\sqrt[4{pd^{2}})\)] ⋮ Congruences for odd class numbers of quadratic fields with odd discriminant ⋮ Historical remark on a theorem of Zhang and Yue ⋮ Divisibility of Class Number of a Real Cubic or Quadratic Field and Its Fundamental Unit ⋮ Hilbert genus fields of real biquadratic fields ⋮ Regulators and class numbers of an infinite family of quintic function fields ⋮ \(\ell\)-class groups of fields in Kummer towers ⋮ Unit groups of maximal orders in totally definite quaternion algebras over real quadratic fields ⋮ Proof of a conjecture of Guy on class numbers ⋮ On abelian 2-ramification torsion modules of quadratic fields

Cites Work

• Residuacity properties of real quadratic units
• Imaginary bicyclic biquadratic fields with cyclic 2-class group
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