Number Theory

A Course in Arithmetic

Name: A Course in Arithmetic
Brand: Springer
SKU: 9780387900407
Price: 6936.00 INR
Availability: InStock
ISBN: 9780387900407

COURSE IN ARITHMETIC CORRECTED

Contributor(s): Serre, J-P. Author Format: Hardback

Hardback · ISBN 9780387900407

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Key Specifications

ISBN	9780387900407
Subtitle	COURSE IN ARITHMETIC CORRECTED
Publisher	Springer
Publication date	November 1978
Language	English
MRP	£54.99 GBP
Page count	132
Item weight	81 g

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 atthe 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.

A Course in Arithmetic

Key Specifications

Serre, J-P. Author

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