Book Details
Format
Hardback or Cased Book
Book Series
Springer Monographs in Mathematics
ISBN-10
1441917314
ISBN-13
9781441917317
Edition
2010 ed.
Publisher
Springer-Verlag New York Inc.
Imprint
Springer-Verlag New York Inc.
Country of Manufacture
GB
Country of Publication
GB
Publication Date
Jun 30th, 2010
Print length
238 Pages
Weight
518 grams
Dimensions
24.30 x 16.40 x 2.00 cms
Product Classification:
AlgebraNumber theory
Ksh 27,000.00
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Topic (A) can be further divided into two types of theories: (a1) Classi?cation over an algebraic number ?eld; At some point we need the Hasse norm theorem for a quadratic extension of a number ?eld, which is included in class ?eld theory. We prove it when the base ?eld is the rational number ?eld to make the book self-contained in that case.
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.
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