{"product_id":"a-course-in-arithmetic-9780387900407","title":"A Course in Arithmetic","description":"\u003cp\u003e • Author(s): J-P Serre\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Number Theory\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003eThis 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.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Hardcover","offer_id":45281215971479,"sku":"9780387900407","price":4366.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9780387900407.webp?v=1769298579","url":"https:\/\/atlanticbooks.com\/products\/a-course-in-arithmetic-9780387900407","provider":"Atlantic Books","version":"1.0","type":"link"}