Table of contents

  • This session has been presented December 01, 2006.

Description

  • Speaker

    Olivier Orcière - Thales

Suite aux travaux de Bhargava sur la généralisation de la loi de Gauss sur le groupes de classes des formes quadratiques binaires, on présentera les quatre formalismes des formes quadratiques binaires utilisés et connus jusqu'à présent:<br/> - le formalisme algébrique de Gauss<br/> - le formalisme projectif de Dirichlet<br/> - le formalisme basé sur les idéaux de Schoof<br/> - le formalisme géométrique de Bhargava<br/> On montrera que ces quatre formalismes sont tous équivalents. On présentera quelques conséquences des travaux de Bhargava du point de vue cryptologique. En particulier, on présente de nouvelles formules de la loi de Gauss grâce à la représentation de Bhargava.<br/> On conclura en présentant une "nouvelle" loi de groupe sur les classes de formes cubiques binaires qui découle directement du formalisme de Bhargava.

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