Advertisement

p-adic Numbers, p-adic Analysis, and Zeta-Functions

  • Neal Koblitz

Part of the Graduate Texts in Mathematics book series (GTM, volume 58)

Table of contents

  1. Front Matter
    Pages i-x
  2. Neal Koblitz
    Pages 1-20
  3. Neal Koblitz
    Pages 52-74
  4. Neal Koblitz
    Pages 75-100
  5. Back Matter
    Pages 121-124

About this book

Introduction

These lecture notes are intended as an introduction to p-adic analysis on the elementary level. For this reason they presuppose as little background as possi­ ble. Besides about three semesters of calculus, I presume some slight exposure to more abstract mathematics, to the extent that the student won't have an adverse reaction to matrices with entries in a field other than the real numbers, field extensions of the rational numbers, or the notion of a continuous map of topolog­ ical spaces. The purpose of this book is twofold: to develop some basic ideas of p-adic analysis, and to present two striking applications which, it is hoped, can be as effective pedagogically as they were historically in stimulating interest in the field. The first of these applications is presented in Chapter II, since it only requires the most elementary properties of Q ; this is Mazur's construction by p means of p-adic integration of the Kubota-Leopoldtp-adic zeta-function, which "p-adically interpolates" the values of the Riemann zeta-function at the negative odd integers. My treatment is based on Mazur's Bourbaki notes (unpublished).

Keywords

Analysis Calc Functions Numbers Zetafunktion algebra calculus construction field function integration matrices p-adische Analysis p-adische Zahl polynomial

Authors and affiliations

  • Neal Koblitz
    • 1
  1. 1.Department of MathematicsHarvard UniversityMassachusettsUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4684-0047-2
  • Copyright Information Springer-Verlag New York 1977
  • Publisher Name Springer, New York, NY
  • eBook Packages Springer Book Archive
  • Print ISBN 978-1-4684-0049-6
  • Online ISBN 978-1-4684-0047-2
  • Series Print ISSN 0072-5285
  • Buy this book on publisher's site