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Catalogue Information
Field name
Details
Dewey Class
512
Title
Arithmetic of Quadratic Forms (EB) / by Goro Shimura.
Author
Shimura, Goro. , 1930-
Other name(s)
SpringerLink (Online service)
Publication
New York, NY : Springer
, 2010.
Physical Details
XII, 240 pages : online resource.
Series
Springer monographs in mathematics
1439-7382
ISBN
9781441917324
Summary Note
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.:
Contents note
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.
System details note
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users).
Internet Site
http://dx.doi.org/10.1007/978-1-4419-1732-4
Links to Related Works
Subject References:
Algebra
.
Forms, Quadratic
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General Algebraic Systems
.
Mathematics
.
Number Theory
.
Authors:
Shimura, Goro. 1930-
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Corporate Authors:
SpringerLink (Online service)
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Series:
Springer monographs in mathematics
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Classification:
512
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