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Issue 1-2: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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1
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Front matter
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2
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Article
DENSITY RESULTS ON FAMILIES OF DIOPHANTINE EQUATIONS WITH FINITELY MANY SOLUTIONS
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3
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Bibliography
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22
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Article
ELLIPTIC SPACES II
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25
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Abstract
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25
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Chapter
1. Introduction
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25
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Chapter
2. The dichotomy
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26
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Chapter
3. Elliptic spaces
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29
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Bibliography
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31
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Article
GÈBRES
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33
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Abstract
Sommaire
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34
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Chapter
Commentaires du rédacteur
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35
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Chapter
§1. Cogèbres et comodules (généralités)
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36
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Chapter
1.1. Cogèbres
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36
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Chapter
1.2. Comodules
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37
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Chapter
1.3. Une formule d'adjonction
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39
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Chapter
1.4. Conséquences d'une hypothèse de platitude
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40
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Chapter
§2. COGÈBRES SUR UN CORPS
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42
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Chapter
2.1. Sous-cogèbres
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42
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Chapter
2.2. Dualité entre cogèbres et algèbres profinies
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43
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Chapter
2.3. Traductions
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45
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Chapter
2.4. Correspondance entre sous-cogèbres et sous-catégories de $Com_C^f$.
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46
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Chapter
2.5. OÙ L'ON CARACTÉRISE $Com_C^f$
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48
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Chapter
§3. Bigèbres
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51
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Chapter
3.1. DÉFINITIONS ET CONVENTIONS
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51
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Chapter
3.2. Correspondance entre comodules et G-modules
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52
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Chapter
3.3. SOUS-BIGÈBRES
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56
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Chapter
3.4. Une interprétation des points de G
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57
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Chapter
3.5. Interprétation de G comme limite projective de groupes ALGÉBRIQUES LINÉAIRES
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60
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Chapter
§4. Enveloppes
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62
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Chapter
4.1. COMPLÉTION D'UNE ALGÈBRE
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62
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Chapter
4.2. La bigèbre d'un groupe
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63
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Chapter
4.3. L'ENVELOPPE D'UN GROUPE RELATIVEMENT À UNE CATÉGORIE DE REPRÉSENTATIONS
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65
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Chapter
§5. Groupes compacts et groupes complexes
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67
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Chapter
5.1. Algébricité des groupes compacts
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67
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Chapter
5.2. L'ENVELOPPE D'UN GROUPE COMPACT
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69
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Chapter
5.3. L'ENVELOPPE COMPLEXE D'UN GROUPE COMPACT
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72
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Chapter
5.4. Retour aux groupes anisotropes
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75
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Chapter
5.5. Groupes de Lie complexes réductifs
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76
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Chapter
Exercices
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79
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Chapter
§1
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79
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Chapter
§2
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80
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Chapter
§3
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80
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Chapter
§4
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81
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Chapter
§5
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83
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Bibliography
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85
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Article
MAXIMALLY COMPLETE FIELDS
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87
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Abstract
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87
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Chapter
I. Introduction
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87
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Chapter
2. Preliminaires
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88
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Chapter
3. Mal'cev-Neumann rings
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89
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Chapter
4. p-adic Mal'cev-Neumann fields
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91
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Chapter
5. Maximality of Mal'cev-Neumann fields
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94
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Chapter
6. Applications
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100
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Chapter
7. Example: the maximally complète immédiate extension of $\bar{Q}_p$
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101
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Bibliography
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105
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Article
HURWITZ QUATERNIONIC INTEGERS AND SEIFERT FORMS
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107
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Chapter
§1. Introduction
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107
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Chapter
§2. The root System $D_4$ and the Hurwitz quaternionic integers
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108
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Chapter
§3. Perfect isometries of H-lattices
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111
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Chapter
§4. Automorphisms of the root System $nD_4$ and perfect isometries
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112
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Chapter
§5. Main Theorem and examples
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116
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Bibliography
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119
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Article
JACOBI FORMS AND SIEGEL MODULAR FORMS: RECENT RESULTS AND PROBLEMS
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121
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Chapter
Introduction
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121
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Chapter
§1. Preliminaries on Siegel modular forms and Jacobi forms
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121
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Chapter
1.1. Siegel modular forms of genus 2
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121
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Chapter
1.2. Jacobi forms
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122
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Chapter
§2. The Maass space
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123
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Chapter
2.1. Results
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123
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Chapter
2.2. Problems
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126
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Chapter
§3. Spinor zeta functions
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128
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Chapter
3.1. Results
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128
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Chapter
1.2 Problems
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130
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Chapter
§4. ESTIMATES FOR FOURIER COEFFICIENTS OF SIEGEL CUSP FORMS
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131
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Chapter
4.1. Results
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131
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Chapter
4.2. PROBLEMS
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132
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Bibliography
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134
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Article
QUICK LOWER BOUNDS FOR REGULATORS OF NUMBER FIELDS
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137
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Abstract
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137
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Rubric
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138
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Bibliography
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141
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Article
THE OKA-PRINCIPLE FOR MAPPINGS BETWEEN RIEMANN SURFACES
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143
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Bibliography
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151
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Article
POLYNÔMES ASSOCIÉS AUX ENDOMORPHISMES DE GROUPES LIBRES
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153
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Abstract
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153
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Abstract
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153
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Chapter
I. Introduction
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154
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Chapter
II. DÉTERMINATION DU NOYAU DE Φ
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157
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Chapter
III. Applications polynomiales laissant λ invariant Caractérisation des σ tels que $Q_\sigma = 1$
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160
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Chapter
IV. Etude des relations $\Phi_\sigma = \Phi_\tau$ et $Q_\sigma = 0$.
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162
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Chapter
V. Autres propriétés des polynômes Qa
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164
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Chapter
VI. Cas d'un groupe libre à plus de deux générateurs
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168
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Bibliography
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174
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Article
THE SUM OF THE CANTOR SET WITH ITSELF
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177
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Bibliography
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178
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Rubric
COMMISSION INTERNATIONALE DE L'ENSEIGNEMENT MATHÉMATIQUE (THE INTERNATIONAL COMMISSION ON MATHEMATICAL INSTRUCTION)
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179
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Chapter
WHAT IS RESEARCH IN MATHEMATICS EDUCATION, AND WHAT ARE ITS RESULTS?
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179
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Chapter
Discussion Document for an ICMI Study
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179
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Chapter
Some Questions About Research
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180
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Chapter
1. What is the specific objet of study in mathematics education?
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181
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Chapter
2. What are the aims of research in mathematics education?
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181
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Chapter
3. WHAT ARE THE SPECIFIC RESEARCH QUESTIONS OR PROBLÉMATIQUES OF RESEARCH IN MATHEMATICS EDUCATION?
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183
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Chapter
4. WHAT ARE THE RESULTS OF RESEARCH IN MATHEMATICS EDUCATION?
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183
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Chapter
5. What criteria should be used to evaluate the results of research in mathematics education?
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185
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Chapter
Call for Papers
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185
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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1
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Back matter
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46
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Back matter
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Back matter
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Issue 3-4: L'ENSEIGNEMENT MATHÉMATIQUE
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Front matter
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Table of Contents
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187
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Front matter
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188
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Article
PONCELET'S THEOREM AND DUAL BILLIARDS
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189
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Bibliography
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194
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Article
IDÉAUX NÉGATIVEMENT RÉDUITS D'UN CORPS QUADRATIQUE RÉEL ET UN PROBLÈME D'EISENSTEIN
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195
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Chapter
§1. Introduction
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195
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Chapter
§2. Classes d'idéaux au sens strict et réduction négative
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196
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Chapter
§3. L'HOMOMORPHISME Θ ET L'APPLICATION Ψ
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204
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Chapter
§4. Exemples numériques
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208
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Bibliography
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210
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Article
COMBINATOIRE ET TYPE TOPOLOGIQUE DES APPLICATIONS POLYNOMIALES DE $C^2$ DANS C
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211
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Chapter
§1. Introduction
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211
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Chapter
§2. COMBINATOIRE ET INFINI
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214
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Chapter
§3. Combinatoire et conjugaison topologique
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216
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Chapter
§4. Utilisations d'un couple de Zariski
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219
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Bibliography
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224
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Article
SMOOTHLY EMBEDDED 2-SPHERES AND EXOTIC 4-MANIFOLDS
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225
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Chapter
1. Introduction
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225
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Chapter
2. The manifolds M(k,l, m)
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227
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Bibliography
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231
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Article
CARROUSEL MONODROMY AND LEFSCHETZ NUMBER OF SINGULARITIES
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233
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Chapter
Introduction
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233
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Chapter
1. The carrousel revisited
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234
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Chapter
2. Lefschetz number via the carrousel
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238
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Chapter
3. Zeta-function and carrousel monodromies
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241
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Bibliography
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246
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Article
REMARKS AND PROBLEMS ON FINITE AND PERIODIC CONTINUED FRACTIONS
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249
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Abstract
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249
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Chapter
§1. A FRUSTRATING QUESTION
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249
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Chapter
§2. A QUESTION CONCERNING PISOT NUMBERS
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250
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Chapter
§3. More questions on $\delta(x^n)$
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251
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Chapter
§4. Related problems
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252
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Chapter
5. More questions
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253
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Chapter
§6. Quadratic surds
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255
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Bibliography
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256
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Article
TREPREAU'S EXAMPLE, A PEDESTRIAN APPROACH
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259
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Chapter
I. Introduction
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259
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Chapter
II. The heart of the matter
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260
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Chapter
III. Lifting to $C^3$
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262
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Chapter
IV. Trepeau's ex ample
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263
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Chapter
V. More
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265
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Chapter
VI. Trepreau does more
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268
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Bibliography
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268
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Article
UNE VERSION NON COMMUTATIVE DES ALGÈBRES DE LIE: LES ALGÈBRES DE LEIBNIZ
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269
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Chapter
1. Algèbres de Leibniz
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271
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Chapter
2. Exemples d'algèbres de Leibniz
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272
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Chapter
3. DÉRIVATIONS ET BIDÉRIVATIONS
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275
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Chapter
4. Extensions abéliennes d'algèbres de Leibniz et représentations
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275
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Chapter
5. Algèbre enveloppante (cf. [L-P]).
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277
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Chapter
6. Cohomologie et homologie d'une algèbre de Leibniz (cf. [L1], [C], [L-P])
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279
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Chapter
7. Calculs de groupes d'homologie HL
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283
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Chapter
8. Liens avec la topologie algébrique
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286
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Chapter
9. Homologie non commutative des algèbres associatives
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288
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Chapter
10. HOMOLOGIE NON COMMUTATIVE DES GROUPES ET K-THÉORIE DES CORPS
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290
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Chapter
11. Intégrer les algèbres de Leibniz
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292
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Bibliography
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292
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Article
SUR LES INVARIANTS DE VASSILIEV DE DEGRÉ INFÉRIEUR OU ÉGAL À 3
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295
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Chapter
0. Introduction
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295
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Chapter
1. Invariants de Vassiliev de degré fini (d'après Vassiliev, Birman et Lin, Bar-Natan)
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296
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Chapter
2. Formalisme relatif aux nœuds de $R^3$ AU-DESSUS D'UNE IMMERSION GÉNÉRIQUE DE $S^1$ DANS $R^2$
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298
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Chapter
3. Relations d'intersection
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302
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Chapter
4. Expression des invariants de Vassiliev de degré inférieur ou égal à 3 en termes de points de croisement
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303
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Bibliography
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316
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Article
ZEROS OF POLYNOMIALS WITH 0, 1 COEFFICIENTS
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317
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Abstract
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317
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Chapter
1. Introduction
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317
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Chapter
2. BOUNDS AND LOCATIONS FOR ZEROS
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326
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Chapter
3. A NEIGHBORHOOD OF THE UNIT CIRCLE
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331
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Chapter
4. $\bar{W}$ IS CONNECTED
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335
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Chapter
5. $\bar{W}$ IS PATH CONNECTED
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339
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Chapter
6. Graphs, computations, and the shape of $\bar{W}$
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343
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Bibliography
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347
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Rubric
BULLETIN BIBLIOGRAPHIQUE
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47
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Back matter
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Front matter
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Index
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Back matter
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Back matter
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Back matter
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