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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 1-5
  3. Fernando Q. Gouvêa
    Pages 7-21
  4. Fernando Q. Gouvêa
    Pages 23-41
  5. Fernando Q. Gouvêa
    Pages 43-85
  6. Fernando Q. Gouvêa
    Pages 87-132
  7. Fernando Q. Gouvêa
    Pages 133-185
  8. Fernando Q. Gouvêa
    Pages 187-233
  9. Back Matter
    Pages 235-305

About this book

Introduction

In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, ab­ stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor­ ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory. This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num­ bers have shown up in other areas of mathematics, and even in physics.

Keywords

Algebra absolute values on fields calculus finite field number theory p-adic analysis p-adic numbers valuations

Authors and affiliations

  • Fernando Q. Gouvêa
    • 1
  1. 1.Department of MathematicsColby CollegeWatervilleUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-59058-0
  • Copyright Information Springer-Verlag Berlin Heidelberg 1997
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-540-62911-5
  • Online ISBN 978-3-642-59058-0
  • Series Print ISSN 0172-5939
  • Series Online ISSN 2191-6675
  • Buy this book on publisher's site