Arithmétique des quaternions

Arithmétique des courbes elliptiques à réduction supersingulière en p

CONTENTS 1. Introduction 2. Fonction L p-adique analytique et congruences provenant de la distribution modulaire 3. Fonction L p-adique arithmétique 4. Conjecture principale et théorème de Kato 5. λ-invariants et µ-invariants 6. Croissance du groupe de Shafarevich-Tate 7. Exemples Numériques A. Démonstration du théorème 3.2 B. Surjectivité de ρ p , Constante de Manin C. Du côté des calculs D. T...

Contribution à l'étude des erreurs d'arrondi en arithmétique à virgule flottante

Arithmétique modulaire pour la cryptographie

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Outils pour une comparaison sans a priori entre arithmétique logarithmique et arithmétique flottante

This paper describes a library of parameterized arithmetic operators for manipulating high-dynamic numbers on FPGA. It support both floating-point and logarithmic representations. Along with its direct interest, that library allow application-specific comparisons of those two number representation systems. It is unbiased in the sense that it tends to reflect the state-of-the-art for both number...

Understanding quaternions

The invention of the calculus of quaternions is a step towards the knowledge of quantities related to space which can only be compared for its importance with the invention of triple coordinates by Descartes. The ideas of this calculus, as distinguished from its operations and symbols, are fitted to be of the greatest use in all parts of science.-Clerk Maxwell, 1869. Quaternions came from Hamil...