© 2000

A Course in p-adic Analysis


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


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.


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

Authors and affiliations

  1. 1.Institut de MathématiquesUniversité de NeuchâtelNeuchâtelSwitzerland

Bibliographic information

  • Book Title A Course in p-adic Analysis
  • Authors Alain M. Robert
  • Series Title Graduate Texts in Mathematics
  • DOI
  • Copyright Information Springer-Verlag New York 2000
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Hardcover ISBN 978-0-387-98669-2
  • Softcover ISBN 978-1-4419-3150-4
  • eBook ISBN 978-1-4757-3254-2
  • Series ISSN 0072-5285
  • Edition Number 1
  • Number of Pages XVI, 438
  • Number of Illustrations 0 b/w illustrations, 0 illustrations in colour
  • Topics Number Theory
  • Buy this book on publisher's site


From the reviews:


"The text ends with a large number of exercises. The writing is extremely clear and very meticulous. The bibliography, which does not attempt to be comprehensive, is adequate. I recommend A. Robert’s book without reservation to anyone who wants to have a reference text on one-variable p-adic analysis that is clear, complete and pleasant to read."


"Robert's book is aimed at an intermediate level between the very specialized monographs and the elementary texts. It has no equal in the marketplace, because it covers practically all of p-adic analysis of one variable (except the rationality of the zeta function of an algebraic variety over a finite field and the theory of p-adic differential equations) and contains numerous results that were accessible only in articles or even in preprints. ...

I recommend A. Robert's book without reservation to anyone who wants to have a reference text on one-variable p-adic analysis that is clear, complete and pleasant to read."
D. Barsky in MathSciNet, August 2001