Discovered at the turn of the 20th century, padic numbers are frequently used by mathematicians and physicists. This text is a selfcontained presentation of basic padic analysis with a focus on analytic topics. It offers many features rarely treated in introductory padic texts such as topological models of padic spaces inside Euclidian space, a special case of Hazewinkel's functional equation lemma, and a treatment of analytic elements.
ISBN  9780387986692   Weight (grammes)  842  ISBN13  9780387986692 (What's this?)   Published in  New York, NY  Publisher  SpringerVerlag New York Inc.   Published in  US  Imprint  SpringerVerlag New York Inc.   Series title  Graduate Texts in Mathematics  Format  Hardback   Series volume part  v.198  Publication date  31 May 2000   Height (mm)  234  DEWEY  512.74   Width (mm)  156  DEWEY edition  DC21   Spine width (mm)  25  Pages  454  



  Preface   
1   padic Numbers   1 
1   The Ring Z[subscript p] of padic Integers   1 
2   The Compact Space Z[subscript p]   7 
3   Topological Algebra   17 
4   Projective Limits   26 
5   The Field Q[subscript p] of padic Numbers   36 
6   Hensel's Philosophy   45 
  Appendix: The padic Solenoid   54 
2   Finite Extensions of the Field of padic Numbers   69 
1   Ultrametric Spaces   69 
2   Absolute Values on the Field Q   85 
3   FiniteDimensional Vector Spaces   90 
4   Structure of padic Fields   97 
  Appendix: Classification of Locally Compact Fields   115 
3   Construction of Universal padic Fields   127 
1   The Algebraic Closure Q[subscript p][superscript a] of Q[subscript p]   127 
2   Definition of a Universal padic Field   134 
3   The Completion C[subscript p] of the Field Q[subscript p][superscript a]   140 
4   Multiplicative Structure of C[subscript p]   146 
  Appendix: Filters and Ultrafilters   152 
4   Continuous Functions on Z[subscript p]   160 
1   Functions of an Integer Variable   160 
2   Continuous Functions on Z[subscript p]   170 
3   Locally Constant Functions on Z[subscript p]   178 
4   Ultrametric Banach Spaces   183 
  More...   
From the reviews: MATHEMATICAL 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 onevariable padic analysis that is clear, complete and pleasant to read." MATHSCINET "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 padic analysis of one variable (except the rationality of the zeta function of an algebraic variety over a finite field and the theory of padic 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 onevariable padic analysis that is clear, complete and pleasant to read." D. Barsky in MathSciNet, August 2001
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