Arithmetic of Quadratic Forms

  • Goro¬†Shimura

Part of the Springer Monographs in Mathematics book series (SMM)

Table of contents

  1. Front Matter
    Pages i-xi
  2. Goro Shimura
    Pages 1-14
  3. Goro Shimura
    Pages 15-45
  4. Goro Shimura
    Pages 47-78
  5. Goro Shimura
    Pages 79-114
  6. Goro Shimura
    Pages 115-151
  7. Goro Shimura
    Pages 153-202
  8. Goro Shimura
    Pages 203-232
  9. Back Matter
    Pages 233-237

About this book

Introduction

This book is divided into two parts. The first part is preliminary and consists of algebraic number theory and the theory of semisimple algebras. There are two principal topics: classification of quadratic forms and quadratic Diophantine equations. The second topic is a new framework which contains the investigation of Gauss on the sums of three squares as a special case. To make the book concise, the author proves some basic theorems in number theory only in some special cases. However, the book is self-contained when the base field is the rational number field, and the main theorems are stated with an arbitrary number field as the base field. So the reader familiar with class field theory will be able to learn the arithmetic theory of quadratic forms with no further references.

Keywords

Algebra Clifford algebras Quadratic Diophantine equations Quadratic forms Quadratic reciprocity law Semisimple algebras Strong approximation Sums of squares number theory

Authors and affiliations

  • Goro¬†Shimura
    • 1
  1. 1.Department of MathematicsPrinceton UniversityPrincetonUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4419-1732-4
  • Copyright Information Springer Science+Business Media, LLC 2010
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4419-1731-7
  • Online ISBN 978-1-4419-1732-4
  • Series Print ISSN 1439-7382
  • About this book