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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 ( 13 ) and ( 17 ) . Finally we compute the Hermite-Humbert constant for the number field ( 13 ) .

Extreme binary forms

Andrzej Białynicki-Birula, Andrzej Schinzel (2010)

Acta Arithmetica

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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 , ) ) . 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 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.