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A Course in p-adic Analysis

  • Alain M. Robert

Part of the Graduate Texts in Mathematics book series (GTM, volume 198)

Table of contents

  1. Front Matter
    Pages i-xv
  2. Alain M. Robert
    Pages 1-68
  3. Alain M. Robert
    Pages 127-159
  4. Alain M. Robert
    Pages 160-216
  5. Alain M. Robert
    Pages 217-279
  6. Alain M. Robert
    Pages 280-365
  7. Alain M. Robert
    Pages 366-417
  8. Back Matter
    Pages 419-440

About this book

Introduction

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.

Keywords

Finite Lemma Mathematica analytic function boundary element method calculus congruence construction differential equation equation field form function functional equation special function

Authors and affiliations

  • Alain M. Robert
    • 1
  1. 1.Institut de MathématiquesUniversité de NeuchâtelNeuchâtelSwitzerland

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4757-3254-2
  • Copyright Information Springer-Verlag New York 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4419-3150-4
  • Online ISBN 978-1-4757-3254-2
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site