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Number theory Vol. 1: tools and diophantine equations

By: Cohen, Henri.
Material type: materialTypeLabelBookPublisher: New York Springer Science+Business Media 2007Description: xxiii, 650 p.ISBN: 9780387499222.Subject(s): Diophantine equations - Textbooks | Number theory - TextbooksDDC classification: 512.7 Summary: The central theme of this graduate - level number theory textbook 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 aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. (http://www.springer.com/mathematics/numbers/book/978-0-387-49922-2)
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The central theme of this graduate - level number theory textbook 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 aspects. The first is the local aspect: one can do analysis in p-adic fields, and here the author starts by looking at solutions in finite fields, then proceeds to lift these solutions to local solutions using Hensel lifting. The second is the global aspect: the use of number fields, and in particular of class groups and unit groups. (http://www.springer.com/mathematics/numbers/book/978-0-387-49922-2)

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