Robert A Course in p-adic Analysis

Erscheinungsjahr 2013
ISBN: 978-1-4757-3254-2
Verlag: Springer US
Format: PDF
Kopierschutz: 1 - PDF Watermark

E-Book, Englisch, Band 198, 438 Seiten, eBook

Reihe: Graduate Texts in Mathematics

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.

Zielgruppe

Graduate

Autoren/Hrsg.

Robert, Alain M.

Inhaltsverzeichnis

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.