Binary quadratic forms and Eichler orders

Montserrat Alsina

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

The inhomogeneous minimum of quadratic forms of signature zero

B. Birch (1958)

Acta Arithmetica

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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 $N \in R$ 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 $R [\sqrt{- c_{f} N}]$ , where $c_{f} \in R$ 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 $D \equiv 0, 1$ 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 genera representing a positive integer

Pierre Kaplan, Kenneth S. Williams (2002)

Acta Arithmetica

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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 $F_{\bar{Π}}$ , the fundamental domain of the modular group, and transforming these forms into the reduced forms with the same discriminant $Δ < 0$ are given.

Erratum “On the computation of quadratic $2$ -class groups”

W. Bosma, P. Stevenhagen (1997)

Journal de théorie des nombres de Bordeaux

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Definite binary quadratic forms with class number one

Meinhard Peters (1980)

Acta Arithmetica

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A note on the distribution of angles associated to indefinite integral binary quadratic forms

Dragan Đokić (2019)

Czechoslovak Mathematical Journal

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To each indefinite integral binary quadratic form $Q$ , we may associate the geodesic in $ℍ$ through the roots of quadratic equation $Q (x, 1)$ . In this paper we study the asymptotic distribution (as discriminant tends to infinity) of the angles between these geodesics and one fixed vertical geodesic which intersects all of them.