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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Provides a self-contained introduction at the post-graduate level in number theory or algebra. After a general introduction the book focuses on p-adic numbers and their use in the theory of numbers. There are also chapters on algebraic number theory, on diophantine equations and on the analysis of a p-adic variable.
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Inside This Book
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First Sentence:
These are generalizations of the ordinary absolute value on the field C of complex numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
first degree extension, field with valuation, convex body theorem, ordinary absolute value, residue class field, strong approximation theorem, ultrametric inequality, minimum polynomial, preparation theorem, algebraic number fields, galois group, finite algebraic extension, principal divisor, cyclic extension, discrete valuation, class field theory, splitting field, fundamental sequence, abelian extension, splitting group, valued fields, prime element Key Phrases - Capitalized Phrases (CAPs): (learn more)
Chinese Remainder Theorem, Hint Exercise, Hint Use New!
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Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
These are generalizations of the ordinary absolute value on the field C of complex numbers. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
first degree extension, field with valuation, convex body theorem, ordinary absolute value, residue class field, strong approximation theorem, ultrametric inequality, minimum polynomial, preparation theorem, algebraic number fields, galois group, finite algebraic extension, principal divisor, cyclic extension, discrete valuation, class field theory, splitting field, fundamental sequence, abelian extension, splitting group, valued fields, prime element Key Phrases - Capitalized Phrases (CAPs): (learn more)
Chinese Remainder Theorem, Hint Exercise, Hint Use New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 3
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41
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- Mathematische Abhandlungen by Oskar Bolza in Back Matter
- Mathematische Werke (AMS Chelsea Publishing) by Gotthold Eisenstein in Back Matter
- Gesammelte Abhandlungen by Issai Schur in Back Matter
- p-adic Numbers: An Introduction (Universitext) by Fernando Quadros Gouvea on page 291, and Back Matter
- Oeuvres - Collected Papers: Volume 2: 1960 - 1971 (French and English Edition) by Jean-Pierre Serre on page 421, and Back Matter
- Software Process Technology: 5th European Workshop, EWSPT '96, Nancy, France, October 9 - 11, 1996. Proceedings (Lecture Notes in Computer Science) by Carlo Montangero on page 83, and page 207
- Reciprocity Laws: From Euler to Eisenstein (Springer Monographs in Mathematics) by Franz Lemmermeyer on page 76, and page 147
- Introduction To Quadratic Forms Over Fields (Graduate Studies in Mathematics) by T. Y. Lam on page 151, and Back Matter
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