### Información del autor

## Autor Cohen, Henri |

### Documentos disponibles escritos por este autor (3)

Refinar búsqueda

Título : Number Theory : Volume I: Tools and Diophantine Equations Tipo de documento: documento electrónico Autores: Cohen, Henri ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 239 Número de páginas: XXIII, 650 p Il.: online resource ISBN/ISSN/DL: 978-0-387-49923-9 Idioma : Inglés ( eng)Palabras clave: Mathematics Algebra Field theory (Physics) Ordered algebraic structures Computer mathematics Algorithms Number Theory and Polynomials Computational Numerical Analysis Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: to Diophantine Equations -- to Diophantine Equations -- Tools -- Abelian Groups, Lattices, and Finite Fields -- Basic Algebraic Number Theory -- p-adic Fields -- Quadratic Forms and Local-Global Principles -- Diophantine Equations -- Some Diophantine Equations -- Elliptic Curves -- Diophantine Aspects of Elliptic Curves En línea: http://dx.doi.org/10.1007/978-0-387-49923-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34501 Number Theory : Volume I: Tools and Diophantine Equations [documento electrónico] / Cohen, Henri ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XXIII, 650 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 239) .ISBN: 978-0-387-49923-9

Idioma : Inglés (eng)

Palabras clave: Mathematics Algebra Field theory (Physics) Ordered algebraic structures Computer mathematics Algorithms Number Theory and Polynomials Computational Numerical Analysis Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: to Diophantine Equations -- to Diophantine Equations -- Tools -- Abelian Groups, Lattices, and Finite Fields -- Basic Algebraic Number Theory -- p-adic Fields -- Quadratic Forms and Local-Global Principles -- Diophantine Equations -- Some Diophantine Equations -- Elliptic Curves -- Diophantine Aspects of Elliptic Curves En línea: http://dx.doi.org/10.1007/978-0-387-49923-9 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34501 ## Ejemplares

Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar

Título : Number Theory : Volume II: Analytic and Modern Tools Tipo de documento: documento electrónico Autores: Cohen, Henri ; SpringerLink (Online service) Editorial: New York, NY : Springer New York Fecha de publicación: 2007 Colección: Graduate Texts in Mathematics, ISSN 0072-5285 num. 240 Número de páginas: XXIII, 596 p Il.: online resource ISBN/ISSN/DL: 978-0-387-49894-2 Idioma : Inglés ( eng)Palabras clave: Mathematics Algebra Field theory (Physics) Ordered algebraic structures Computer mathematics Algorithms Number Theory and Polynomials Computational Numerical Analysis Order, Lattices, Algebraic Structures Clasificación: 51 Matemáticas Resumen: 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 Nota de contenido: Analytic Tools -- Bernoulli Polynomials and the Gamma Function -- Dirichlet Series and L-Functions -- p-adic Gamma and L-Functions -- Modern Tools -- Applications of Linear Forms in Logarithms -- Rational Points on Higher-Genus Curves -- The Super-Fermat Equation -- The Modular Approach to Diophantine Equations -- Catalan’s Equation En línea: http://dx.doi.org/10.1007/978-0-387-49894-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34499 Number Theory : Volume II: Analytic and Modern Tools [documento electrónico] / Cohen, Henri ; SpringerLink (Online service) . - New York, NY : Springer New York, 2007 . - XXIII, 596 p : online resource. - (Graduate Texts in Mathematics, ISSN 0072-5285; 240) .ISBN: 978-0-387-49894-2

Idioma : Inglés (eng)

Palabras clave: Clasificación: 51 Matemáticas Resumen: Nota de contenido: Analytic Tools -- Bernoulli Polynomials and the Gamma Function -- Dirichlet Series and L-Functions -- p-adic Gamma and L-Functions -- Modern Tools -- Applications of Linear Forms in Logarithms -- Rational Points on Higher-Genus Curves -- The Super-Fermat Equation -- The Modular Approach to Diophantine Equations -- Catalan’s Equation En línea: http://dx.doi.org/10.1007/978-0-387-49894-2 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=34499 ## Ejemplares

Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar Solving Polynomial Equations / SpringerLink (Online service) ; Bronstein, Manuel ; Cohen, Arjeh M ; Cohen, Henri ; Eisenbud, David ; Sturmfels, Bernd ; Dickenstein, Alicia ; Emiris, Ioannis Z (2005)

Título : Solving Polynomial Equations : Foundations, Algorithms, and Applications Tipo de documento: documento electrónico Autores: SpringerLink (Online service) ; Bronstein, Manuel ; Cohen, Arjeh M ; Cohen, Henri ; Eisenbud, David ; Sturmfels, Bernd ; Dickenstein, Alicia ; Emiris, Ioannis Z Editorial: Berlin, Heidelberg : Springer Berlin Heidelberg Fecha de publicación: 2005 Colección: Algorithms and Computation in Mathematics, ISSN 1431-1550 num. 14 Número de páginas: XIV, 426 p. 44 illus., 11 illus. in color Il.: online resource ISBN/ISSN/DL: 978-3-540-27357-8 Idioma : Inglés ( eng)Palabras clave: Mathematics Computer science Algebra Algorithms Symbolic and Algebraic Manipulation Clasificación: 51 Matemáticas Resumen: The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems Nota de contenido: to residues and resultants -- Solving equations via algebras -- Symbolic-numeric methods for solving polynomial equations and applications -- An algebraist’s view on border bases -- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks -- Algorithms and their complexities -- Toric resultants and applications to geometric modelling -- to numerical algebraic geometry -- Four lectures on polynomial absolute factorization En línea: http://dx.doi.org/10.1007/b138957 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35276 Solving Polynomial Equations : Foundations, Algorithms, and Applications [documento electrónico] / SpringerLink (Online service) ; Bronstein, Manuel ; Cohen, Arjeh M ; Cohen, Henri ; Eisenbud, David ; Sturmfels, Bernd ; Dickenstein, Alicia ; Emiris, Ioannis Z . - Berlin, Heidelberg : Springer Berlin Heidelberg, 2005 . - XIV, 426 p. 44 illus., 11 illus. in color : online resource. - (Algorithms and Computation in Mathematics, ISSN 1431-1550; 14) .ISBN: 978-3-540-27357-8

Idioma : Inglés (eng)

Palabras clave: Mathematics Computer science Algebra Algorithms Symbolic and Algebraic Manipulation Clasificación: 51 Matemáticas Resumen: The subject of this book is the solution of polynomial equations, that is, s- tems of (generally) non-linear algebraic equations. This study is at the heart of several areas of mathematics and its applications. It has provided the - tivation for advances in di?erent branches of mathematics such as algebra, geometry, topology, and numerical analysis. In recent years, an explosive - velopment of algorithms and software has made it possible to solve many problems which had been intractable up to then and greatly expanded the areas of applications to include robotics, machine vision, signal processing, structural molecular biology, computer-aided design and geometric modelling, as well as certain areas of statistics, optimization and game theory, and b- logical networks. At the same time, symbolic computation has proved to be an invaluable tool for experimentation and conjecture in pure mathematics. As a consequence, the interest in e?ective algebraic geometry and computer algebrahasextendedwellbeyonditsoriginalconstituencyofpureandapplied mathematicians and computer scientists, to encompass many other scientists and engineers. While the core of the subject remains algebraic geometry, it also calls upon many other aspects of mathematics and theoretical computer science, ranging from numerical methods, di?erential equations and number theory to discrete geometry, combinatorics and complexity theory. Thegoalofthisbookistoprovideageneralintroduction tomodernma- ematical aspects in computing with multivariate polynomials and in solving algebraic systems Nota de contenido: to residues and resultants -- Solving equations via algebras -- Symbolic-numeric methods for solving polynomial equations and applications -- An algebraist’s view on border bases -- Tools for computing primary decompositions and applications to ideals associated to Bayesian networks -- Algorithms and their complexities -- Toric resultants and applications to geometric modelling -- to numerical algebraic geometry -- Four lectures on polynomial absolute factorization En línea: http://dx.doi.org/10.1007/b138957 Link: https://biblioteca.cunef.edu/gestion/catalogo/index.php?lvl=notice_display&id=35276 ## Ejemplares

Signatura Medio Ubicación Sub-localización Sección Estado ningún ejemplar