Local fields
by Cassels, J. W. S., (John William Scott)
"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-contain…
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- Full title :Local fields / J.W.S. Cassels.
Summary
"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"--Publisher description.
Read More ↓Edition Statements
- Publication Date:1986.
Publication Statements
- Publisher(s):Cambridge University Press
- Place of Publication:Cambridge [Cambridgeshire]
- Language:eng
- Publication Date:1986.
The Physical Object
- Description:xiv, 360 pages : : illustrations ; : 24 cm.
Edition Identifiers
- ISBN:0521304849, 9780521304849, 0521315255, 9780521315258
- oclc:ocm12262799
- LC Classification:QA247
- Dewey Decimal:512/.3
Table of Contents
Notational conventions -- Valuations -- General properties -- Archimedean valuations -- Non Archimedean valuations, simple properties -- Embedding theorem -- Transcendental extension, factorization -- Algebraic extensions (complete fields) -- Padic fields -- Algebraic extensions (incomplete fields) -- Algebraic number fields -- Diophantine equations -- Advanced analysis -- A theorem of Borel and Dwork.
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