Hermite's constant for quadratic number fields.

Baeza, Ricardo; Coulangeon, Renaud; Icaza, Maria Ines; O'Ryan, Manuel

Displaying similar documents to “Hermite's constant for quadratic number fields.”

On the computation of Hermite-Humbert constants for real quadratic number fields

Michael E. Pohst, Marcus Wagner (2005)

Journal de Théorie des Nombres de Bordeaux

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We present algorithms for the computation of extreme binary Humbert forms in real quadratic number fields. With these algorithms we are able to compute extreme Humbert forms for the number fields $ℚ (\sqrt{13})$ and $ℚ (\sqrt{17})$ . Finally we compute the Hermite-Humbert constant for the number field $ℚ (\sqrt{13})$ .

Composition of binary quadratic forms

Irving Kaplansky (1968)

Studia Mathematica

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Extreme binary forms

Andrzej Białynicki-Birula, Andrzej Schinzel (2010)

Acta Arithmetica

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On the minimal points of perfect quadratic forms.

R.A. Rankin (1964)

Mathematische Zeitschrift

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Minimal forms with respect to function fields of conics.

D.W. Hoffmann, J. Van Geel (1995)

Manuscripta mathematica

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Cyclotomic quadratic forms

François Sigrist (2000)

Journal de théorie des nombres de Bordeaux

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Voronoï ’s algorithm is a method for obtaining the complete list of perfect $n$ -dimensional quadratic forms. Its generalization to $G$ -forms has the advantage of running in a lower-dimensional space, and furnishes a finite, and complete, classification of $G$ -perfect forms ( $G$ is a finite subgroup of $G L (n, ℤ))$ . We study the standard, $φ (m)$ -dimensional irreducible representation of the cyclic group $C_{m}$ of order $m$ , and give the, often new, densest $G$ -forms. Perfect cyclotomic forms are completely classified...

The construction of perfect and extreme forms I

E. Barnes (1959)

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.