Henri Cohen: Number Theory | Taschenbuch

Cover: 9781441923882 | Number Theory | Volume II: Analytic and Modern Tools | Henri Cohen

Rückseite: 9781441923882 | Number Theory | Volume II: Analytic and Modern Tools | Henri Cohen

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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.

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:	Importe , Mathematik
Rubrik:	Naturwissenschaften & Technik
Medium:	Taschenbuch
Inhalt:	xxiii 596 S.
ISBN-13:	9781441923882
ISBN-10:	1441923888
Sprache:	Englisch
Einband:	Kartoniert / Broschiert
Autor:	Cohen, Henri
Auflage:	Softcover reprint of hardcover 1st edition 2007
Hersteller:	Springer US Springer New York
Verantwortliche Person für die EU:	Springer Verlag GmbH, Tiergartenstr. 17, D-69121 Heidelberg, juergen.hartmann@springer.com
Maße:	235 x 155 x 34 mm
Von/Mit:	Henri Cohen
Erscheinungsdatum:	19.11.2010
Gewicht:	0,937 kg