A Course in Arithmetic

A Course in Arithmetic
Author :
Publisher : Springer Science & Business Media
Total Pages : 126
Release :
ISBN-10 : 9781468498844
ISBN-13 : 1468498843
Rating : 4/5 (843 Downloads)

Book Synopsis A Course in Arithmetic by : J-P. Serre

Download or read book A Course in Arithmetic written by J-P. Serre and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 126 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.


A Course in Arithmetic Related Books

A Course in Arithmetic
Language: en
Pages: 126
Authors: J-P. Serre
Categories: Mathematics
Type: BOOK - Published: 2012-12-06 - Publisher: Springer Science & Business Media

GET EBOOK

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 number
A Course in Arithmetic
Language: en
Pages: 118
Authors: J-P. Serre
Categories: Mathematics
Type: BOOK - Published: 1996-11-07 - Publisher: Springer

GET EBOOK

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 number
A First Course in Modular Forms
Language: en
Pages: 462
Authors: Fred Diamond
Categories: Mathematics
Type: BOOK - Published: 2006-03-30 - Publisher: Springer Science & Business Media

GET EBOOK

This book introduces the theory of modular forms, from which all rational elliptic curves arise, with an eye toward the Modularity Theorem. Discussion covers el
A Course in Number Theory and Cryptography
Language: en
Pages: 245
Authors: Neal Koblitz
Categories: Mathematics
Type: BOOK - Published: 2012-09-05 - Publisher: Springer Science & Business Media

GET EBOOK

This is a substantially revised and updated introduction to arithmetic topics, both ancient and modern, that have been at the centre of interest in applications
Arithmetic Algebraic Geometry
Language: en
Pages: 588
Authors: Brian David Conrad
Categories: Mathematics
Type: BOOK - Published: - Publisher: American Mathematical Soc.

GET EBOOK

The articles in this volume are expanded versions of lectures delivered at the Graduate Summer School and at the Mentoring Program for Women in Mathematics held