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- About this Textbook
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Kurt Hensel (1861-1941) discovered the p-adic numbers around the turn of the century. These exotic numbers (or so they appeared at first) are now well-established in the mathematical world and used more and more by physicists as well. This book offers a self-contained presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features which are not treated in other introductory p-adic analysis texts are topological models of p-adic spaces inside Euclidean space, a construction of spherically complete fields, a p-adic mean value theorem and some consequences, a special case of Hazewinkel's functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.
- Reviews
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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
- Table of contents (7 chapters)
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p-adic Numbers
Pages 1-68
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Finite Extensions of the Field of p-adic Numbers
Pages 69-126
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Construction of Universal p-adic Fields
Pages 127-159
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Continuous Functions on Z p
Pages 160-216
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Differentiation
Pages 217-279
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Table of contents (7 chapters)
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Bibliographic Information
- Bibliographic Information
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- Book Title
- A Course in p-adic Analysis
- Authors
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- Alain M. Robert
- Series Title
- Graduate Texts in Mathematics
- Series Volume
- 198
- Copyright
- 2000
- Publisher
- Springer-Verlag New York
- Copyright Holder
- Springer Science+Business Media New York
- eBook ISBN
- 978-1-4757-3254-2
- DOI
- 10.1007/978-1-4757-3254-2
- Hardcover ISBN
- 978-0-387-98669-2
- Softcover ISBN
- 978-1-4419-3150-4
- Series ISSN
- 0072-5285
- Edition Number
- 1
- Number of Pages
- XVI, 438
- Topics
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