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Displaying similar documents to “Non-Markovian quadratic forms obtained by homogenization”

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 , ℝ ) and a Shimura curve X ( D , N ) . We associate to 𝒪 ( D , N ) a set ℋ ( 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 ℋ ( 𝒪 ( D , N ) ) . In particular, the classification theory of primitive integral binary quadratic forms by SL ( 2 , ℤ ) is recovered. Explicit fundamental domains for Γ ( D , N ) allow the characterization...

Remarks on the quasiconvex envelope of some functions depending on quadratic forms

M. Bousselsal, H. Le Dret (2002)

Bollettino dell'Unione Matematica Italiana

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We compute the quasiconvex envelope of certain functions defined on the space M m ⁢ n of real m × n matrices. These functions are basically functions of a quadratic form on M m ⁢ n . The quasiconvex envelope computation is applied to densities that are related to the James-Ericksen elastic stored energy function.