Displaying similar documents to “Binary quadratic forms and Eichler orders”

On integral representations by totally positive ternary quadratic forms

Elise Björkholdt (2000)

Journal de théorie des nombres de Bordeaux

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Let K be a totally real algebraic number field whose ring of integers R is a principal ideal domain. Let f ( x 1 , x 2 , x 3 ) be a totally definite ternary quadratic form with coefficients in R . We shall study representations of totally positive elements N ∈ R by f . We prove a quantitative formula relating the number of representations of N by different classes in the genus of f to the class number of R [ - c f N ] , where c f ∈ R is a constant depending only on f . We give an algebraic proof of a classical result of H. Maass...

On the computation of quadratic 2 -class groups

Wieb Bosma, Peter Stevenhagen (1996)

Journal de théorie des nombres de Bordeaux

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We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer D ≡ 0 , 1 mod 4 and the factorization of D , computes the structure of the 2 -Sylow subgroup of the class group of the quadratic order of discriminant D in random polynomial time in log D .

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.