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Graduate Texts in Mathematics

A Course in Arithmetic

Authors: Serre, J-P.

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eBook $49.99
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  • ISBN 978-1-4684-9884-4
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  • ISBN 978-0-387-90040-7
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About this Textbook

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.

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)


Table of contents (7 chapters)

Buy this book

eBook $49.99
price for USA in USD (gross)
  • ISBN 978-1-4684-9884-4
  • Digitally watermarked, DRM-free
  • Included format: PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $64.95
price for USA in USD
  • ISBN 978-0-387-90040-7
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
A Course in Arithmetic
Authors
Series Title
Graduate Texts in Mathematics
Series Volume
7
Copyright
1973
Publisher
Springer-Verlag New York
Copyright Holder
Springer-Verlag New York
eBook ISBN
978-1-4684-9884-4
DOI
10.1007/978-1-4684-9884-4
Hardcover ISBN
978-0-387-90040-7
Series ISSN
0072-5285
Edition Number
1
Number of Pages
IX, 119
Additional Information
Original French edition with the title: Cours d'arithmetique
Topics