Number theory Vol. 1: tools and diophantine equations

By:

Cohen, Henri

Material type: Text

TextPublication details: 2007 Springer Science+Business Media New YorkDescription: xxiii, 650 pISBN:

9780387499222

Subject(s):

DDC classification:

512.7 C6N8

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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Holdings
Item type	Current library	Call number	Status	Date due	Barcode	Item holds
Book	Ahmedabad	512.7 C6N8 (Browse shelf(Opens below))	Available		174150

Total holds: 0

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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