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  • Cited by 90
Publisher:
Cambridge University Press
Online publication date:
June 2012
Print publication year:
1986
Online ISBN:
9781139171885
DOI:
https://doi.org/10.1017/CBO9781139171885
Subjects:
Mathematics (general), Mathematics, Number Theory, Algebra
Series:
London Mathematical Society Student Texts (3)
Information

Book description

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.

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