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A course in p-adic analysis

Author: Alain Robert
Publisher: New York : Springer, ©2000.
Series: Graduate texts in mathematics, 198.
Edition/Format:   Print book : EnglishView all editions and formats
Summary:
"This book offers a presentation of basic p-adic analysis. The author is especially interested in the analytical topics in this field. Some of the features that 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  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Alain Robert
ISBN: 0387986693 9780387986692 1441931503 9781441931504
OCLC Number: 42290178
Description: xv, 437 pages : illustrations ; 25 cm.
Contents: 1. p-adic Numbers --
1. The Ring Z[subscript p] of p-adic Integers --
2. The Compact Space Z[subscript p] --
3. Topological Algebra --
4. Projective Limits --
5. The Field Q[subscript p] of p-adic Numbers --
6. Hensel's Philosophy --
Appendix: The p-adic Solenoid --
2. Finite Extensions of the Field of p-adic Numbers --
1. Ultrametric Spaces --
2. Absolute Values on the Field Q --
3. Finite-Dimensional Vector Spaces --
4. Structure of p-adic Fields --
Appendix: Classification of Locally Compact Fields --
3. Construction of Universal p-adic Fields --
1. The Algebraic Closure Q[subscript p][superscript a] of Q[subscript p] --
2. Definition of a Universal p-adic Field --
3. The Completion C[subscript p] of the Field Q[subscript p][superscript a] --
4. Multiplicative Structure of C[subscript p] --
Appendix: Filters and Ultrafilters --
4. Continuous Functions on Z[subscript p] --
1. Functions of an Integer Variable --
2. Continuous Functions on Z[subscript p] --
3. Locally Constant Functions on Z[subscript p] --
4. Ultrametric Banach Spaces --
5. Umbral Calculus --
6. Generating Functions --
5. Differentiation --
1. Differentiability --
2. Restricted Formal Power Series --
3. The Mean Value Theorem --
4. The Exponentiel and Logarithm --
5. The Volkenborn Integral --
6. Analytic Functions and Elements --
1. Power Series --
2. Zeros of Power Series --
3. Rational Functions --
4. Analytic Elements --
7. Special Functions, Congruences --
1. The Gamma Function [Gamma][subscript p] --
2. The Artin-Hasse Exponential --
3. The Hazewinkel Theorem and Honda Congruences --
Basic Principles of Ultrametric Analysis.
Series Title: Graduate texts in mathematics, 198.
Responsibility: Alain M. Robert.
More information:

Abstract:

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  Read more...

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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, Read more...

 
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