## 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

- 1.Department of MathematicsPrinceton UniversityPrincetonUSA

### Bibliographic information