The Number of Real Quadratic Fields Having Units of Negative Norm

DOI10.1080/10586458.1993.10504272zbMath0792.11041OpenAlexW1983003491MaRDI QIDQ4285755

Peter Stevenhagen

Publication date: 31 July 1994

Published in: Experimental Mathematics (Search for Journal in Brave)

Full work available at URL: https://projecteuclid.org/euclid.em/1048516217

zbMATH Keywords

Pell equationRedei matrices4-class groupdensity of discriminants of quadratic fields

Mathematics Subject Classification ID

Quadratic extensions (11R11) Quadratic and bilinear Diophantine equations (11D09) Class numbers, class groups, discriminants (11R29)

Related Items (20)

A Note on the Negative Pell Equation ⋮ Semicomplete Arithmetic Sequences, Division of Hypercubes, and the Pell Constant ⋮ Frobenius distributions for real quadratic orders ⋮ Torus bundles not distinguished by TQFT invariants. With an appendix by Louis Funar and Andrei Rapinchuk ⋮ The 8-rank of the narrow class group and the negative Pell equation ⋮ Redei reciprocity, governing fields and negative Pell ⋮ On counting polynomials over finite fields ⋮ A POLYNOMIAL ANALOGUE OF LANDAU'S THEOREM AND RELATED PROBLEMS ⋮ Non-Pólya bi-quadratic fields with an Euclidean ideal class ⋮ Unit signature ranks in real biquadratic and multiquadratic number fields ⋮ Explicit methods in number theory. Abstracts from the workshop held July 18--24, 2021 (hybrid meeting) ⋮ On the negative Pell equation ⋮ Density computations for real quadratic units ⋮ Hilbert genus fields of real biquadratic fields ⋮ On the computation of quadratic 2-class groups ⋮ On the prime density of Lucas sequences ⋮ Spins of prime ideals and the negative Pell equation ⋮ Quaternionic Artin representations and nontraditional arithmetic statistics ⋮ The negative Pell equation and Pythagorean triples ⋮ On unit signatures and narrow class groups of odd degree abelian number fields

Cites Work

• The 4-class ranks of quadratic fields
• Divisibility by 2-powers of certain quadratic class numbers
• Über die Lösbarkeit der Gleichung \(t^2-Du^2=-4\)
• Some Density Results for Negative Pell Equations; an Application of Graph Theory
• Orthogonal Matrices Over Finite Fields
• Bedingtes Artinsches Symbol mit Anwendung in der Klassenkörpertheorie
• Die 2-Ringklassengruppe des quadratischen Zahlkörpers und die Theorie der Pellschen Gleichung
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