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A Course in p-adic Analysis (Graduate Texts in Mathematics), by Alain M. Robert
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Discovered at the turn of the 20th century, p-adic numbers are frequently used by mathematicians and physicists. This text is a self-contained presentation of basic p-adic analysis with a focus on analytic topics. It offers many features rarely treated in introductory p-adic texts such as topological models of p-adic spaces inside Euclidian space, a special case of Hazewinkel’s functional equation lemma, and a treatment of analytic elements.
- Sales Rank: #1616168 in Books
- Published on: 2000-05-31
- Original language: English
- Number of items: 1
- Dimensions: 9.21" h x 1.00" w x 6.14" l, 3.99 pounds
- Binding: Hardcover
- 438 pages
- ISBN13: 9780387986692
- Condition: USED - Like New
- Notes: 100% Satisfaction Guarantee. Tracking provided on most orders. Buy with Confidence! Millions of books sold!
Review
From the reviews:
MATHEMATICAL REVIEWS
"The text ends with a large number of exercises. The writing is extremely clear and very meticulous. The bibliography, which does not attempt to be comprehensive, is adequate. I recommend A. Robert’s book without reservation to anyone who wants to have a reference text on one-variable p-adic analysis that is clear, complete and pleasant to read."
MATHSCINET
"Robert's book is aimed at an intermediate level between the very specialized monographs and the elementary texts. It has no equal in the marketplace, because it covers practically all of p-adic analysis of one variable (except the rationality of the zeta function of an algebraic variety over a finite field and the theory of p-adic differential equations) and contains numerous results that were accessible only in articles or even in preprints. ...
I recommend A. Robert's book without reservation to anyone who wants to have a reference text on one-variable p-adic analysis that is clear, complete and pleasant to read."
D. Barsky in MathSciNet, August 2001
Most helpful customer reviews
1 of 1 people found the following review helpful.
The only good textbook exposition of the p-adic solenoid
By Jordan Bell
This is the most complete single place to learn about the p-adic numbers. Two other works that are similar are Gouvêa, p-adic Numbers: An Introduction (Universitext), and Schikhof, Ultrametric Calculus: An Introduction to p-Adic Analysis (Cambridge Studies in Advanced Mathematics), and I like Roberts the most of these three.
This book has what is probably the longest exposition in any book on the p-adic solenoid, as the appendix to Chapter 1. The group of p-adic integers is a compact abelian group that can be defined as an inverse limit of finite groups, and this way of thinking about the p-adic integers (rather than as formal power series or as a completion using the p-adic metric) make the p-adic solenoid a natural object to work with. The p-adic solenoid is a compact abelian group that is an inverse limit of compact abelian groups. Some of its properties are that the real numbers and the p-adic numbers are embedded naturally in it, and that it is the Pontryagin dual of the discrete group Z[1/p] of rational numbers whose denominator is some power of the prime p. Anyone who is interested in harmonic analysis on locally compact abelian groups should read this appendix on the p-adic solenoid.
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