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Local Fields : London Mathematical Society Student Texts - J. W. S. Cassels

Local Fields

London Mathematical Society Student Texts

By: J. W. S. Cassels, J. Bruce (Editor)

Paperback Published: 20th October 1986
ISBN: 9780521315258
Number Of Pages: 376

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The p-adic numbers, the earliest of local fields, were introduced by Hensel some 70 years ago as a natural tool in algebra number theory. Today the use of this and other local fields pervades much of mathematics, yet these simple and natural concepts, which often provide remarkably easy solutions to complex problems, are not as familiar as they should be. This book, based on postgraduate lectures at Cambridge, is meant to rectify this situation by providing a fairly elementary and self-contained introduction to local fields. After a general introduction, attention centres on the p-adic numbers and their use in number theory. There follow chapters on algebraic number theory, diophantine equations and on the analysis of a p-adic variable. This book will appeal to undergraduates, and even amateurs, interested in number theory, as well as to graduate students.

Preface
Leitfaden
Notational conventions
Introduction
General properties
Archimedean valuations
Non archimedean valuations
Embedding theorem
Transcendental extensions
Algebraic extensions
p-adic fields
Algebraic extensions
Algebraic number fields
Diophantine equations
Advanced analysis
A theorem of Borel and work
Appendices
References
Index
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9780521315258
ISBN-10: 0521315255
Series: London Mathematical Society Student Texts
Audience: Professional
Format: Paperback
Language: English
Number Of Pages: 376
Published: 20th October 1986
Publisher: Cambridge University Press
Country of Publication: GB
Dimensions (cm): 22.8 x 15.2  x 2.1
Weight (kg): 0.55

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