A Course in p-adic Analysis - Robert, Alain M.

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Résumé :
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 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 functional equation lemma, a remainder formula for the Mahler expansion, and most importantly a treatment of analytic elements.

Sommaire:

• p-adic numbers
• Finite extensions of the field of p-adic numbers
• Construction of universal p-adic fields
• Continuous functions on Zp
• Differentiation
• Analytic functions and elements
• Special functions congruences