A Course in p-adic Analysis

Couverture
Springer Science & Business Media, 17 avr. 2013 - 438 pages
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.
 

Table des matières

Preface
1
Multiplicative Structure of
4
2
12
Torsion of the Solenoid
40
The padic Solenoid
55
Topological Properties of the Solenoid
61
Finite Extensions of the Field of padic Numbers
69
Classification of Locally Compact Fields
82
Locally Constant Functions on
178
Ultrametric Banach Spaces
189
4
269
Analytic Functions and Elements
280
69
322
2
323
Analytic Elements
337
Exercises for Chapter VI
348

The Modulus is a Strict Homomorphism
118
Exercises for Chapter III
123
1
125
1
131

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