Article

An explicit construction of initial perfect quadratic forms over some families of totally real number fields

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ANTS-VIII'08: Proceedings of the 8th international conference on Algorithmic number theory

Pages 240 - 252

Published: 17 May 2008 Publication History

Abstract

In this paper we construct initial perfect quadratic formsover certain families of totally real number fields K. We assume that thenumber field K is either the maximal totally real subfield of a cyclotomicfield Q(ζ_n), where 3 χ n is the product of distinct odd primes p₁, . . . , p_k,or K = Q(√m₁, . . . , √m_k), where m₁, . . . , m_k are pairwise relativelyprime, square-free positive integers with all or all but one congruent to 1modulo 4. These perfect forms can be used to find all perfect quadraticforms of given rank (up to equivalence and proportion) over the field Kby applying the generalization of Voronoi's algorithm.

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Index Terms

An explicit construction of initial perfect quadratic forms over some families of totally real number fields
1. Theory of computation
  1. Randomness, geometry and discrete structures

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Published In

ANTS-VIII'08: Proceedings of the 8th international conference on Algorithmic number theory

May 2008

454 pages

ISBN:3540794557

Editors:
Alfred J. Van Der Poorten
ceNTRe for Number Theory Research, Killara, NSW, Australia
,
Andreas Stein
Carl von Ossietzky Universität Oldenburg, Institut für Mathematik, Oldenburg, Germany

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Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 17 May 2008

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