Displaying similar documents to “On the computation of quadratic 2 -class groups”

Binary quadratic forms and Eichler orders

Montserrat Alsina (2005)

Journal de Théorie des Nombres de Bordeaux

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For any Eichler order 𝒪 ( D , N ) of level N in an indefinite quaternion algebra of discriminant D there is a Fuchsian group Γ ( D , N ) SL ( 2 , ) and a Shimura curve X ( D , N ) . We associate to 𝒪 ( D , N ) a set ( 𝒪 ( D , N ) ) of binary quadratic forms which have semi-integer quadratic coefficients, and we develop a classification theory, with respect to Γ ( D , N ) , for primitive forms contained in ( 𝒪 ( D , N ) ) . In particular, the classification theory of primitive integral binary quadratic forms by SL ( 2 , ) is recovered. Explicit fundamental domains for Γ ( D , N ) allow the characterization...

The connection between quadratic forms and the extended modular group

Ahmet Tekcan, Osman Bizim (2003)

Mathematica Bohemica

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In this paper some properties of quadratic forms whose base points lie in the point set F Π ¯ , the fundamental domain of the modular group, and transforming these forms into the reduced forms with the same discriminant Δ < 0 are given.