[Graduate Texts in Mathematics] Number Theory Volume 239 || Diophantine Aspects of Elliptic Curves

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• Book ID: 121375870
• Publisher: Springer New York
• Year: 2007
• Tongue: English
• Weight: 856 KB
• Edition: 1st Edition
• Category: Article
• ISBN: 0387499237
• DOI: 10.1007/978-0-387-49923-9_8

✦ Synopsis

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.