- Series: Graduate Texts in Mathematics (Book 198)
- Hardcover: 438 pages
- Publisher: Springer; 2000 edition (May 31, 2000)
- Language: English
- ISBN-10: 0387986693
- ISBN-13: 978-0387986692
- Product Dimensions: 6.1 x 1 x 9.2 inches
- Shipping Weight: 1.8 pounds (View shipping rates and policies)
- Average Customer Review: 1 customer review
- Amazon Best Sellers Rank: #2,710,510 in Books (See Top 100 in Books)
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A Course in p-adic Analysis (Graduate Texts in Mathematics) 2000th Edition
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From the 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."
"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
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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.