Course in Arithmetic (eBook)

J-P. Serre (Autor)

eBook Download: PDF

2012
Springer New York (Verlag)
978-1-4684-9884-4 (ISBN)

Infos

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 "e;analytic"e; methods (holomor- phic functions). Chapter VI gives the proof of the "e;theorem on arithmetic progressions"e; 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.

Produkt-Details

• Erscheint lt. Verlag: 6.12.2012
• Sprache: englisch
• Themenwelt: Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
• ISBN-10: 1-4684-9884-3 / 1468498843
• ISBN-13: 978-1-4684-9884-4 / 9781468498844