A Course in Arithmetic: 7 (Graduate Texts in Mathematics, 7) - Tapa dura

Serre, J-P.

 
9780387900407: A Course in Arithmetic: 7 (Graduate Texts in Mathematics, 7)
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ISBN 10: 0387900403 ISBN 13: 9780387900407
Editorial: Springer, 1978

Sinopsis

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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Críticas

“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)

Críticas

J.-P. Serre A Course in Arithmetic "The book is carefully writtena "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."a "AMERICAN SCIENTIST

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Editorial
Springer
Año de publicación
1978
Idioma
Inglés
ISBN 10 
0387900403
ISBN 13 
9780387900407
Encuadernación
Tapa dura
Número de edición
5
Número de páginas
132
Contacto del fabricante
ProductSafety@springernature.com
ProductSafety@springernature.com

Poststr. 9
Darmstadt
64293
Alemania

Otras ediciones populares con el mismo título

9783540900405: A Course in Arithmetic: Vol 7 (Graduate Texts in Mathematics)

Edición Destacada

ISBN 10:  3540900403 ISBN 13:  9783540900405
Editorial: Springer-Verlag Berlin and Heide..., 1996
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