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(2020/06/07 12:09:05時点)

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Number Theory, Vol. 1: Tools and Diophantine Equations (Graduate Texts in Mathematics)

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詳しい情報
出版社: Springer
ハードカバー: 673 ページ / 15.6 x 3.7 x 23.4 cm / 2470.0 g
ISBN-10: 0387499229  ISBN-13: 9780387499222  [この本のウィジェットを作る]

紹介

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.

目次

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.
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