A Course in p-adic Analysis

Alain M. Robert (Autor)

Buch | Softcover

438 Seiten

2010 | Softcover reprint of hardcover 1st ed. 2000
Springer-Verlag New York Inc.
978-1-4419-3150-4 (ISBN)

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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.

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.

Erscheint lt. Verlag	19.11.2010
Reihe/Serie	Graduate Texts in Mathematics ; 198
Zusatzinfo	XVI, 438 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
	Mathematik / Informatik ► Mathematik ► Arithmetik / Zahlentheorie
	Mathematik / Informatik ► Mathematik ► Wahrscheinlichkeit / Kombinatorik
ISBN-10	1-4419-3150-3 / 1441931503
ISBN-13	978-1-4419-3150-4 / 9781441931504
Zustand	Neuware