Number Theory

Volume II: Analytic and Modern Tools
1. Auflage. Softcover version of original hardcover Auflage 2007
ISBN: 978-1-4419-2388-2
Verlag: Springer

Buch, Englisch, Band 240, 596 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 937 g

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Research

Autoren/Hrsg.

Cohen, Henri

Fachgebiete

• Mathematik | Informatik Mathematik Algebra Lineare und multilineare Algebra, Matrizentheorie
• Mathematik | Informatik Mathematik Mathematische Analysis Moderne Anwendungen der Analysis
• Mathematik | Informatik Mathematik Algebra Zahlentheorie

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.