A course in arithmetic

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Its objective is the classification of quadratic forms over the field of rational numbers (Hasse-Minkowski theorem). Chapter V applies the preceding results to integral quadratic forms of discriminant ± I. Chapter VII deals with modular forms, and in particular, with theta functions. Some of the quadratic forms of Chapter V reappear here.



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.

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Taal: en

Bindwijze: Hardcover

Oorspronkelijke releasedatum: 29 november 1978

Aantal pagina's: 132

Illustraties: Nee

Hoofdauteur: J-P. Serre

Tweede Auteur: Jean-Pierre Serre

Co Auteur: J-P Serre

Hoofduitgeverij: Springer-Verlag New York Inc.

Editie: 1st Corrected ed. 1973. Corr. 3rd printing 1996

Extra groot lettertype: Nee

Product breedte: 156 mm

Product hoogte: 11 mm

Product lengte: 234 mm

Studieboek: Nee

Verpakking breedte: 162 mm

Verpakking hoogte: 14 mm

Verpakking lengte: 238 mm

Verpakkingsgewicht: 449 g

EAN: 9780387900407

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