数論・第Ⅰ巻：ツールとディオファントス方程式 Number Theory, Volume I : Tools and Diophantine Equations (Graduate Texts in Mathematics) 〈Vol. 239〉

Cohen, Henri

Springer（2007/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 550 p.
• 言語 ENG
• 商品コード 9780387499222
• DDC分類 512

基本説明

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.

Full Description

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. The book contains more than 350 exercises and the text is largely self-contained. 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.

Contents

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.