WorldCat Identities

Cohen, Henri

Overview
Works: 30 works in 229 publications in 3 languages and 3,473 library holdings
Genres: Conference papers and proceedings  Handbooks and manuals  Textbooks 
Roles: Author, Editor, Translator, Thesis advisor, Interviewee, Opponent, Creator
Publication Timeline
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Most widely held works by Henri Cohen
A course in computational algebraic number theory by Henri Cohen( Book )

54 editions published between 1993 and 2015 in 3 languages and held by 763 WorldCat member libraries worldwide

Describes 148 algorithms that are fundamental for number-theoretic computations including computations related to algebraic number theory, elliptic curves, primality testing, and factoring. A complete theoretical introduction is given for each subject, reducing prerequisites to a minimum. The detailed description of each algorithm allows immediate
Advanced topics in computational number theory by Henri Cohen( Book )

17 editions published between 1999 and 2013 in English and held by 447 WorldCat member libraries worldwide

The present book addresses a number of specific topics in computational number theory whereby the author is not attempting to be exhaustive in the choice of subjects. The book is organized as follows. Chapters 1 and 2 contain the theory and algorithms concerning Dedekind domains and relative extensions of number fields, and in particular the generalization to the relative case of the round 2 and related algorithms. Chapters 3, 4, and 5 contain the theory and complete algorithms concerning class field theory over number fields. The highlights are the algorithms for computing the structure of (Z_K/m)^*, of ray class groups, and relative equations for Abelian extensions of number fields using Kummer theory. Chapters 1 to 5 form a homogeneous subject matter which can be used for a 6 months to 1 year graduate course in computational number theory. The subsequent chapters deal with more miscellaneous subjects. Written by an authority with great practical and teaching experience in the field, this book together with the author's earlier book will become the standard and indispensable reference on the subject
Number theory by Henri Cohen( Book )

4 editions published between 2007 and 2010 in English and held by 342 WorldCat member libraries worldwide

"A unique collection of topics centered on a unifying topic. Includes more than 350 exercises. Text is largely self-contained. The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the third part of the book, including many interesting and original applications. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. These chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, Samir Siksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms. The book contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and contain many important additional results."--Publisher's website
Algorithmic number theory : second internati[o]nal symposium, ANTS-II, Talence, France, May 18-23, 1996 : proceedings by Henri Cohen( Book )

20 editions published in 1996 in English and Undetermined and held by 299 WorldCat member libraries worldwide

"This book constitutes the refereed post-conference proceedings of the Second International Algorithmic Number Theory Symposium, ANTS-II, held in Talence, France in May 1996. The 35 revised full papers included in the book were selected from a variety of submissions. They cover a broad spectrum of topics and report state-of-the-art research results in computational number theory and complexity theory. Among the issues addressed are number fields computation, Abelian varieties, factoring algorithms, finite fields, elliptic curves, algorithm complexity, lattice theory, and coding."--PUBLISHER'S WEBSITE
Number theory by Henri Cohen( Book )

48 editions published between 2007 and 2010 in English and Undetermined and held by 137 WorldCat member libraries worldwide

Preface.- Introduction to Diophantine Equations.- Abelian Groups, Lattices, and Finite Fields.-Basic Algebraic Number Theory.- p-adic Fields.-Quadratic Forms and Local-Global Principles.- Some Diophantine Equations.- Eilliptic Curves.- Diophantine Aspects of Elliptic Curves.- Bibliography.- Index.<br>
Number theory by Henri Cohen( Book )

23 editions published between 2007 and 2011 in English and Undetermined and held by 105 WorldCat member libraries worldwide

The central theme of this graduate-level number theory textbook is the solution of Diophantine equations, i.e., equations or systems of polynomial equations which must be solved in integers, rational numbers or more generally in algebraic numbers. This theme, in particular, is the central motivation for the modern theory of arithmetic algebraic geometry. In this text, this is considered through three aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. This classical subject is here illustrated through a wide range of examples. The third aspect deals with specific classes of equations, and in particular the general and Diophantine study of elliptic curves, including 2 and 3-descent and the Heegner point method. These subjects form the first two parts, forming Volume I. The study of Bernoulli numbers, the gamma function, and zeta and L-functions, and of p-adic analogues is treated at length in the third part of the book, including many interesting and original applications. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five chapters on these techniques forming the fourth part, which together with the third part forms Volume II. These chapters were written by Yann Bugeaud, Guillaume Hanrot, Maurice Mignotte, Sylvain Duquesne, Samir Siksek, and the author, and contain material on the use of Galois representations, points on higher-genus curves, the superfermat equation, Mihailescu's proof of Catalan's Conjecture, and applications of linear forms in logarithms. The book contains 530 exercises of varying difficulty from immediate consequences of the main text to research problems, and contain many important additional results
Modular forms : a classical approach by Henri Cohen( Book )

6 editions published in 2017 in English and held by 102 WorldCat member libraries worldwide

The theory of modular forms is a fundamental tool used in many areas of mathematics and physics. It is also a very concrete and ""fun"" subject in itself and abounds with an amazing number of surprising identities. This comprehensive textbook, which includes numerous exercises, aims to give a complete picture of the classical aspects of the subject, with an emphasis on explicit formulas. After a number of motivating examples such as elliptic functions and theta functions, the modular group, its subgroups, and general aspects of holomorphic and nonholomorphic modular forms are explained, with a
Handbook of elliptic and hyperelliptic curve cryptography by Henri Cohen( Book )

22 editions published between 2005 and 2014 in English and held by 97 WorldCat member libraries worldwide

"The Handbook of Elliptic and Hyperelliptic Curve Cryptography introduces the theory and algorithms involved in curve-based cryptography. After a very detailed exposition of the mathematical background, it provides ready-to-implement algorithms for the arithmetic of elliptic and hyperelliptic curves and the computation of pairings. It explores methods for point counting and constructing curves with the complex multiplication method. It also surveys generic methods to compute discrete logarithms and details index calculus methods for hyperelliptic curves as well as transfers of discrete logarithm problems for special curves. It ends up with concrete realizations of cryptosystems in smart cards, including efficient implementation in hardware and side-channel attacks as well as countermeasures."--BOOK JACKET
Class field theory : from theory to practice by Georges Gras( Book )

3 editions published between 2003 and 2005 in English and French and held by 16 WorldCat member libraries worldwide

"Global class field theory is a major achievement of algebraic number theory, based on the functorial properties of the reciprocity map and the existence theorem. The author works out the consequences and the practical use of these results by giving detailed studies and illustrations of classical subjects (classes, ideles, ray class fields, symbols, reciprocity laws, Hasse's principles, the Grunwald-Wang theorem, Hilbert's towers ...). This book, intermediary between the classical literature published in the sixties and the recent computational literature, gives much material in an elementary way, and is suitable for students, researchers, and all who are fascinated by this theory."--Jacket
Formes modulaires à une et deux variables by Henri Cohen( Book )

4 editions published in 1976 in French and Undetermined and held by 10 WorldCat member libraries worldwide

FORMES MODULAIRES SUR GAMMA O(4). APPLICATIONS DU CALCUL DES COEFFICIENTS DE FOURIER DES SERIES D'EISENSTEIN-HECKE. COMBINATOIRE ET DERIVEES DE FORMES MODULAIRES. IDENTITES FAISANT INTERVENIR LES VALEURS AUX ENTIERS NEGATIFS DES FONCTIONS L DE CARACTERES QUADRATIQUES. FORMES MODULAIRES DE HILBERT A DEUX VARIABLES ASSOCIEES A UNE FORME A UNE VARIABLE. DESCRIPTION DES GROUPES GAMMA N
From number theory to physics by Michel Waldschmidt( Book )

3 editions published between 1992 and 1995 in English and held by 7 WorldCat member libraries worldwide

Various developments in physics have involved many questions related to number theory, in an increasingly direct way. This trend is especially visible in two broad families of problems, namely, field theories, and dynamical systems and chaos. The 14 chapters of this book are extended, self-contained versions of expository lecture courses given at a school on "Number Theory and Physics" held at Les Houches for mathematicians and physicists. Most go as far as recent developments in the field. Some adapt an original pedagogical viewpoint
Théorie algorithmique des nombres et équations diophantiennes by Henri Cohen( Book )

1 edition published in 2005 in French and held by 6 WorldCat member libraries worldwide

Number theoryn1 by Henri Cohen( )

1 edition published in 2007 in English and held by 5 WorldCat member libraries worldwide

Number theoryn2 by Henri Cohen( )

1 edition published in 2007 in English and held by 5 WorldCat member libraries worldwide

L'état des maths( Visual )

3 editions published between 2008 and 2010 in French and held by 3 WorldCat member libraries worldwide

Minoration de la hauteur de Néron-Tate sur les variétés abéliennes sur la conjecture de Lang et Silverman by Fabien Mehdi Pazuki( Book )

1 edition published in 2008 in French and held by 2 WorldCat member libraries worldwide

Cette thèse est consacrée à l'étude d'une conjecture de Lang et Silverman de minoration de la hauteur de Néron-Tate sur les variétés abéliennes sur les corps de nombres. Le premier chapitre décrit le matériel nécessaire à l'étude des chapitres suivants et fixe les notations et normalisations. On montre dans le second chapitre que la conjecture est vraie pour certaines classes de variétés abéliennes de dimension 2, en particulier pour les jacobiennes ayant potentiellement bonne réduction et restant loin des produits de courbes elliptiques dans l'espace de modules. Le second chapitre renferme aussi des corollaires allant dans la direction de la conjecture de borne uniforme sur la torsion et de majoration uniforme du nombre de points rationnels d'une courbe de genre 2. Le troisième chapitre généralise les résultats de minoration du second chapitre aux jacobiennes de courbes huperelliptiques de genre g ≥ 2. Le quatrième chapitre contient une étude de la restriction des scalaires à la Weil et une étude asymptotique de la hauteur des points de Heegner sur les jacobiennes de courbes modulaires. Le cinquième chapitre est une annexe contenant des formules explicites utiles pour la dimension 2 et un paragraphe sur un raisonnement par isogénies
Calculs effectifs des points entiers et rationnels sur les courbes by Sylvain Duquesne( Book )

1 edition published in 2001 in French and held by 2 WorldCat member libraries worldwide

Cette thèse est constituée de trois parties indépendantes concernant la détermination des points rationnels et entiers sur les courbes algébriques. Nous nous sommes particulièrement intéressé aux aspects algorithmiques de ces problèmes. Dans la première partie, nous avons considéré la famille des courbes elliptiques définies par les "simplest cubic fields". Nous décrivons une méthode pour calculer exactement tous les points en-tiers sur ces courbes. Une étude expérimentale sur un grand nombre de courbes nous a amené à observer certains phénomènes que nous prouvons par la suite. En particulier, nous donnons explicitement tous les points entiers sur ces courbes lorsque leur rang vaut 1. La deuxième partie concerne le calcul des points rationnels sur les courbes de plus grand genre. Dans le but de calculer ces points lorsque le rang de la jacobienne est supérieur au genre de la courbe, Flynn et Wetherell utilisent le groupe formel d'une courbe elliptique de rang l. Nous développons une version explicite du théorème de préparation de Weierstrass pour généraliser cette méthode au cas des courbes elliptiques de rang supérieur à 1, ce qui permet de traiter de nouvelles équations diophantiennes. La dernière partie de cette thèse consiste à calculer les traces de la loi de groupe sur la variété de Kummer d'une courbe hyperelliptique de genre 3 définie par un polynôme de degré 7. Ces traces permettent de construire une fonction hauteur sur la jacobienne. Nous pouvons alors espérer d'une part en déduire une procédure effective de calcul du sous-groupe de torsion et d'autre part effectuer des descentes infinies
Variations sur un thème de Davanport et Heilbronn : formes cubiques, corps cubiques, et groupes de classes des corps quadratiques by Karim Belabas( Book )

1 edition published in 1996 in French and held by 1 WorldCat member library worldwide

NOUS PRECISONS UNE CONSTRUCTION DE DAVENPORT ET HEILBRONN, QUI PERMET DE MANIPULER EXPLICITEMENT DES FAMILLES DE CORPS CUBIQUES ET LEURS INVARIANTS SIMPLES. NOUS DRESSONS DES TABLES ETENDUES ET DONNONS DES RESULTATS DE DENSITE SUR LES DISCRIMINANTS CUBIQUES ET LA 3-PARTIE DES GROUPES DE CLASSES DES CORPS QUADRATIQUES, AVEC DES TERMES D'ERREUR EFFECTIFS. ON EXAMINE PLUS PARTICULIEREMENT LE CAS DES DISCRIMINANTS AYANT PEU DE FACTEURS PREMIERS. NOUS ETUDIONS ENSUITE LE P-RANG DES CORPS QUADRATIQUES DANS CE CONTEXTE, PUIS LE 3-RANG DES CORPS DE NOMBRES, SOUS LE MODELE PROBABILISTE DE COHEN-LENSTRA-MARTINET
Aspects algorithmiques du système de calcul arithmétique en multiprécision PARI by Christian Batut( Book )

1 edition published in 1989 in French and held by 1 WorldCat member library worldwide

CE TRAVAIL EXPOSE LA STRUCTURE ET UN CERTAIN NOMBRE D'ALGORITHMES DU SYSTEME DE CALCUL EN MULTIPRECISION PARI, ECRIT EN LANGAGE ASSEMBLEUR 68020 ET EN LANGAGE C. LE SYSTEME PARI PERMET D'EFFECTUER DES CALCULS SUR LES NOMBRES ENTIERS ET LES NOMBRES REELS EN MULTIPLECISION. IL CONTIENT UNE BIBLIOTHEQUE DES PRINCIPALES FONCTIONS ARITHMETIQUES ET TRANSCENDANTES CALCULEES EN PRECISION ARBITRAIRE. IL PEUT EGALEMENT EFFECTUER DES CALCULS SUR LES OBJETS MATHEMATIQUES USUELS: NOMBRES RATIONNELS, NOMBRES COMPLEXES, NOMBRES ALGEBRIQUES, NOMBRES P-ADIQUES, ENTIERS MODULO, POLYNOMES, DEVELOPPEMENTS EN SERIE, VECTEURS ET MATRICES. UNE BIBLIOTHEQUE DE PROGRAMMES PERMET A UN UTILISATEUR D'AVOIR ACCES A LA PLUPART DES OPERATIONS ET FONCTIONS IMPORTANTES SUR CES OBJETS. D'AUTRE PART UN CALCULATEUR PERMET D'UTILISER DIRECTEMENT AU CLAVIER TOUTE LA BIBLIOTHEQUE. ENFIN LA COMPARAISON AVEC D'AUTRES SYSTEMES MONTRE QUE DANS SON DOMAINE DE COMPETENCE, PARI EST ENVIRON DIX FOIS PLUS RAPIDE QUE LES SYSTEMES ANALOGUES
Computability of Julia sets by Mark Braverman( )

2 editions published in 2009 in Undetermined and English and held by 0 WorldCat member libraries worldwide

"Computational hardness of Julia sets is the main subject of this book. By definition, a computable set in the plane can be visualized on a computerscreen with an arbitrarily high magnification. There are countless programs to draw Julia sets. Yet, as the authors have discovered, it is possible to constructively produce examples of quadratic polynomials, whose Julia sets are not computable. This result is striking it says that while a dynamical system can be described numerically with an arbitrary precision, the picture of the dynamics cannot be visualized. The book summarizes the present knowledge about the computational properties of Julia sets in a self-contained way. It is accessible to experts and students with interest in theoretical computer science or dynamical systems."--Jacket
 
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A course in computational algebraic number theory
Alternative Names
Cohen, H.

Henri Cohen Frans wiskundige

Henri Cohen fransk matematikar

Henri Cohen fransk matematiker

Henri Cohen französischer Mathematiker

Henri Cohen French mathematician

Henri Cohen matemático francés

Henri Cohen mathématicien français

Анри Коэн

هنري كوهن رياضياتي فرنسي

アンリ・コーエン (数論学者)

亨利·科恩 (數論家)

Languages
English (197)

French (12)

German (1)

Covers
Advanced topics in computational number theoryNumber theoryAlgorithmic number theory : second internati[o]nal symposium, ANTS-II, Talence, France, May 18-23, 1996 : proceedingsNumber theoryNumber theoryHandbook of elliptic and hyperelliptic curve cryptographyClass field theory : from theory to practiceFrom number theory to physicsComputability of Julia sets