# A Course in Arithmetic (Graduate Texts in Mathematics)

## J-P. Serre

Valutazione media 4,35
( su 23 valutazioni fornite da Goodreads )

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.

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Language Notes:

Text: English (translation)
Original Language: French

Review:

“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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## 1.A Course in Arithmetic (Graduate Texts in Mathematics)

Editore: Springer (1973)
ISBN 10: 0387900411 ISBN 13: 9780387900414
Nuovi Paperback Quantità: 1
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Murray Media
(North Miami Beach, FL, U.S.A.)
Valutazione libreria

Descrizione libro Springer, 1973. Paperback. Condizione libro: New. Codice libro della libreria P110387900411

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