A Course in Arithmetic

By: J-P. Serre

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Hardcover | 29 November 1978 | Edition Number 5

At a Glance

Hardcover
132 Pages

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24.2 x 16.5 x 1.5

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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. The first three chapters contain some preliminaries: quadratic reciprocity law, p-adic fields, Hilbert symbols. Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. These forms occur in various questions: modular functions, differential topology, finite groups. The second part (Chapters VI and VII) uses "analytic" methods (holomor phic functions). Chapter VI gives the proof of the "theorem on arithmetic progressions" due to Dirichlet; this theorem is used at a critical point in the first part (Chapter Ill, no. 2.2). Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here. The two parts correspond to lectures given in 1962 and 1964 to second year students at the Ecole Normale Superieure. A redaction of these lectures in the form of duplicated notes, was made by J.-J. Sansuc (Chapters I-IV) and J.-P. Ramis and G. Ruget (Chapters VI-VII). They were very useful to me; I extend here my gratitude to their authors.

Industry Reviews

"The book is a showcase of how some results in classical number theory (the Arithmetic of the title) can be derived quickly using abstract algebra. ... There are a reasonable number of worked examples, and they are very well-chosen. ... this book will expand your horizons, but you should already have a good knowledge of algebra and of classical number theory before you begin." (Allen Stenger, MAA Reviews, maa.org, July, 2016)

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis Number Theory

Algebraic Methods: Finite fields
p-adic fields
Hilbert symbol
Quadratic forms over Qp, and over Q
Integral quadratic forms with discriminant -1
Analytic Methods: The theorem on arithmetic progressions
Modular forms
Bibliography
Indices
Table of Contents provided by Publisher. All Rights Reserved.

A Course in Arithmetic

At a Glance

Hardcover

Industry Reviews

Shipping

How to return your order

Defective items

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