Number Theory

Volume I: Tools and Diophantine Equations
1. Auflage. Softcover version of original hardcover Auflage 2007
ISBN: 978-1-4419-2390-5
Verlag: Springer

Buch, Englisch, 650 Seiten, Previously published in hardcover, Format (B × H): 155 mm x 235 mm, Gewicht: 1013 g

Reihe: Graduate Texts in Mathematics

The central theme of this book 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. Much more sophisticated techniques have been brought to bear on the subject of Diophantine equations, and for this reason, the author has included five appendices on these techniques. The book contains more than 350 exercises and the text is largely self-contained.

Zielgruppe

Research

Autoren/Hrsg.

Cohen, Henri

Fachgebiete

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

Inhaltsverzeichnis

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.