{"product_id":"9780387900407","title":"Course in Arithmetic","description":"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.","brand":"J-P. Serre","offers":[{"title":"Default Title","offer_id":45770214703422,"sku":"9780387900407","price":1797.4,"currency_code":"ZAR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0784\/4357\/7662\/products\/9780387900407_82089ea2-4537-46e8-ad51-e569fbde2d97.jpg?v=1707250543","url":"https:\/\/exclusivebooks.co.za\/products\/9780387900407","provider":"Exclusive Books Online","version":"1.0","type":"link"}