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A Course in p-adic Analysis

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概要 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 mo...re 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.続きを見る
目次 1 p-adic Numbers
2 Finite Extensions of the Field of p-adic Numbers
3 Construction of Universal p-adic Fields
4 Continuous Functions on Zp
5 Differentiation
6 Analytic Functions and Elements
7 Special Functions, Congruences
Specific References for the Text
Tables
Basic Principles of Ultrametric Analysis
Conventions, Notation, Terminology.
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登録日 2020.06.27
更新日 2020.06.28