A Course in p-adic Analysis

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Springer Science & Business Media, May 31, 2000 - Mathematics - 438 pages
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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.
 

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Contents

Projective Limits
26
The Field Qp of padic Numbers
36
Hensels Philosophy
45
The padic Solenoid
54
Exercises for Chapter I
63
Finite Extensions of the Field of padic Numbers
69
Absolute Values on the Field Q
85
Structure of padic Fields
97
Continuous Functions on Zp
160
Umbral Calculus
195
Exercises for Chapter IV
212
Restricted Formal Power Series
233
The Mean Value Theorem
241
The Exponentiel and Logarithm
251
The Volkenborn Integral
263
Exercises for Chapter V
276

Classification of Locally Compact Fields
115
Exercises for Chapter II
123
Definition of a Universal padic Field
134
Special Functions Congruences
366
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