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A Course in Arithmetic by J-P. Serre (Hardcover, 1996)

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This book is divided into two parts. The first one is purely algebraic. Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). It is achieved in Chapter IV.

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Serre's A Course in Arithmetic is a concentrated, modern introduction to basically three areas of number theory, quadratic forms, Dirichlet's density theorem, and modular forms. The first edition was very well accepted and is now one of the leading introductory texts on the advanced undergraduate or beginning graduate level.From the reviews: ...The book is carefully written - in particular very much self-contained. As was the intention of the author, it is easily accessible to graduate or even undergraduate students, yet even the advanced mathematician will enjoy reading it. The last chapter, more difficult for the beginner, is an introduction to contemporary problems. American Scientist