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This title in other editions

Arithmetic of Quadratic Forms (Springer Monographs in Mathematics)

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Synopses & Reviews

Publisher Comments:

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.

Synopsis:

This book examines algebraic number theory and the theory of semisimple algebras. It covers classification over an algebraic number field and classification over the ring of algebraic integers.

Table of Contents

Preface.- Notation and Terminology.- The Quadratic Reciprocity Law.- Arithmetic in an Algebraic Number Field.- Various Basic Theorems.- Algebras Over a Field.- Quadratic Forms Over a Field.- Deeper Arithmetic of Quadratic Forms.- Quadratic Diophantine Equations.- References.- Index.-

Product Details

ISBN:
9781441917317
Author:
Shimura, Goro
Publisher:
Springer
Subject:
Algebra - Abstract
Subject:
Number Theory
Subject:
Algebra - General
Subject:
Clifford algebras
Subject:
Quadratic Diophantine equations
Subject:
Quadratic Forms
Subject:
Quadratic reciprocity law
Subject:
Semisimple algebras
Subject:
Strong approximation
Subject:
Sums of squares
Subject:
Algebra
Subject:
General Algebraic Systems
Subject:
Mathematics-Number Theory
Copyright:
Edition Description:
2010
Series:
Springer Monographs in Mathematics
Publication Date:
20100630
Binding:
HARDCOVER
Language:
English
Pages:
250
Dimensions:
235 x 155 mm 1170 gr

Related Subjects

Science and Mathematics » Mathematics » Algebra » General
Science and Mathematics » Mathematics » General
Science and Mathematics » Mathematics » Number Theory

Arithmetic of Quadratic Forms (Springer Monographs in Mathematics) New Hardcover
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$180.25 In Stock
Product details 250 pages Springer - English 9781441917317 Reviews:
"Synopsis" by , This book examines algebraic number theory and the theory of semisimple algebras. It covers classification over an algebraic number field and classification over the ring of algebraic integers.
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