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Cover: 9781441923882 | Number Theory | Volume II: Analytic and Modern Tools | Henri Cohen
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Number Theory
Volume II: Analytic and Modern Tools
Taschenbuch von Henri Cohen
Sprache: Englisch

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Beschreibung
This book deals with several aspects of what is now called "explicit number theory." The central theme 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 of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.
This book deals with several aspects of what is now called "explicit number theory." The central theme 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 of its most basic aspects. The local aspect, global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject.
Zusammenfassung
This book deals with several aspects of what is now called "explicit number theory." The central theme 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 of its most basic aspects. The first is the local aspect, the second is the global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject, and embodies in a beautiful way the local and global aspects of Diophantine problems. This unique collection of topics contains more than 350 exercises and its text is largely self-contained.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xxiii
596 S.
ISBN-13: 9781441923882
ISBN-10: 1441923888
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Cohen, Henri
Auflage: Softcover reprint of hardcover 1st ed. 2007
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 34 mm
Von/Mit: Henri Cohen
Erscheinungsdatum: 19.11.2010
Gewicht: 0,937 kg
Artikel-ID: 107219611
Zusammenfassung
This book deals with several aspects of what is now called "explicit number theory." The central theme 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 of its most basic aspects. The first is the local aspect, the second is the global aspect, and the third aspect is the theory of zeta and L-functions. This last aspect can be considered as a unifying theme for the whole subject, and embodies in a beautiful way the local and global aspects of Diophantine problems. This unique collection of topics contains more than 350 exercises and its text is largely self-contained.
Inhaltsverzeichnis
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.
Details
Erscheinungsjahr: 2010
Fachbereich: Arithmetik & Algebra
Genre: Mathematik
Rubrik: Naturwissenschaften & Technik
Medium: Taschenbuch
Reihe: Graduate Texts in Mathematics
Inhalt: xxiii
596 S.
ISBN-13: 9781441923882
ISBN-10: 1441923888
Sprache: Englisch
Ausstattung / Beilage: Paperback
Einband: Kartoniert / Broschiert
Autor: Cohen, Henri
Auflage: Softcover reprint of hardcover 1st ed. 2007
Hersteller: Springer New York
Springer US, New York, N.Y.
Graduate Texts in Mathematics
Maße: 235 x 155 x 34 mm
Von/Mit: Henri Cohen
Erscheinungsdatum: 19.11.2010
Gewicht: 0,937 kg
Artikel-ID: 107219611
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