A Course in Arithmetic (Graduate Texts in Mathematics, Vol. 7) (Graduate Texts in Mathematics, 7)

Serre, J-P.

ISBN 10: 0387900403 / ISBN 13: 9780387900407

Published by Springer, 1978

About this Item

Connecting readers with great books since 1972. Used textbooks may not include companion materials such as access codes, etc. May have condition issues including wear and notes/highlighting. We ship orders daily and Customer Service is our top priority!

Seller Inventory # S_471351265

Bibliographic Details

• Title: A Course in Arithmetic (Graduate Texts in Mathematics, Vol. 7) (Graduate Texts in Mathematics, 7)
• Publisher: Springer
• Publication Date: 1978
• Language: English
• ISBN 10: 0387900403
• ISBN 13: 9780387900407
• Binding: Hardcover
• Condition: Acceptable

About this title

Synopsis

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.

Language Notes

Text: English (translation)
Original Language: French