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Bounds for Class Numbers of Quadratic Orders

  • Stéphane Louboutin
  • Richard A. Mollin
Part of the Mathematics and Its Applications book series (MAIA, volume 325)

Abstract

Let Δ be the discriminant of the order O Δ in Q(\(\sqrt \Delta \)) having conductor f and let the class group be denoted by C Δ having order h Δ, the class number of O Δ. Furthermore [α, β] denotes the module {α x + ß y : x, yZ}, and a primitive ideal I in O Δ is one which can be written as [a, b + ω Δ] where a = N(I) is the norm of I and ω Δ = f ω 0 + h for integers f and h with \(\omega _0 = \left( {\sigma - 1 + \sqrt {D_0 } } \right)/\sigma .\). Here D 0 is the radicand, i.e. the square-free kernel of Δ, and we have that σ = 2 if D 0 ≡ 1 mod 4 or σ = 1 otherwise.

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Copyright information

© Springer Science+Business Media Dordrecht 1995

Authors and Affiliations

  • Stéphane Louboutin
    • 1
  • Richard A. Mollin
    • 2
  1. 1.Département de MathématiquesUniversité de CaenCaen CedexFrance
  2. 2.Department of Mathematics and StatisticsUniversity of CalgaryCalgaryCanada

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