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p-adic Numbers

An Introduction

  • Fernando Q. Gouvêa

Part of the Universitext book series (UTX)

Table of contents

  1. Front Matter
    Pages i-vi
  2. Fernando Q. Gouvêa
    Pages 1-4
  3. Fernando Q. Gouvêa
    Pages 5-19
  4. Fernando Q. Gouvêa
    Pages 21-39
  5. Fernando Q. Gouvêa
    Pages 41-83
  6. Fernando Q. Gouvêa
    Pages 85-116
  7. Fernando Q. Gouvêa
    Pages 117-169
  8. Fernando Q. Gouvêa
    Pages 171-219
  9. Back Matter
    Pages 221-284

About this book

Introduction

p-adic numbers are of great theoretical importance in number theory, since they allow the use of the language of analysis to study problems relating toprime numbers and diophantine equations. Further, they offer a realm where one can do things that are very similar to classical analysis, but with results that are quite unusual. The book should be of use to students interested in number theory, but at the same time offers an interesting example of the many connections between different parts of mathematics. The book strives to be understandable to an undergraduate audience. Very little background has been assumed, and the presentation is leisurely. There are many problems, which should help readers who are working on their own (a large appendix with hints on the problem is included). Most of all, the book should offer undergraduates exposure to some interesting mathematics which is off the beaten track. Those who will later specialize in number theory, algebraic geometry, and related subjects will benefit more directly, but all mathematics students can enjoy the book.

Keywords

Rack calculus completions diophantine equation diophantine equations equation local fields mathematics metric spaces non-archimedian analysis number theory p-adic analysis p-adic numbers presentation prime number

Authors and affiliations

  • Fernando Q. Gouvêa
    • 1
  1. 1.Department of Mathematics and Computer ScienceColby CollegeWatervilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-662-22278-2
  • Copyright Information Springer-Verlag Berlin Heidelberg 1993
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-56844-5
  • Online ISBN 978-3-662-22278-2
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site