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

Serre, Jean-Pierre

ISBN 10: 0387900403 / ISBN 13: 9780387900407

Editore: Springer, Berlin, 1973

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117 pp. Tightly bound. Corners not bumped. No ownership markings. Published without dust jacket. NOTE: The reason for the lower "good" rating is because the boards show some discoloration from age and use. The spine shows some fading. I saw some erasable pencil notations on one or two pages but left them as they appear to be a correction to an equation. This copy is smyth sewn. Smyth sewing is a method of bookbinding where groups of folded pages (referred to as signatures) are stitched together using binder thread. Each folded signature is sewn together individually with multiple stitches and then joined with other signatures to create the complete book block. This is the traditional and best method of bookbinding. Codice articolo 031533

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Titolo: Course in Arithmetic (Graduate Texts in ...

Casa editrice: Springer, Berlin

Data di pubblicazione: 1973

Legatura: Hardcover

Condizione: Good

Condizione sovraccoperta: Published Without Dust Jacket

Descrizione articolo

Riassunto:

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.

Recensione:

“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)