A Course in p-adic Analysis

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Springer Science & Business Media, 17.04.2013 - 438 Seiten
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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Inhalt

padic Numbers
1
The Compact Space
7
Topological Algebra
17
Hensels Philosophy
45
Finite Extensions of the Field of padic Numbers
69
Construction of Universal padic Fields
127
Continuous Functions on Zp
160
Differentiation
217
Analytic Functions and Elements
280
Special Functions Congruences
366
Specific References for the Text 419
418
Tables
425
Index
435
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