导语

  

内容提要

  

    高等数学中有各种数，有理数、实数、复数和p进数，其中p进数最不被人所知，但其在数论和数学其它领域广泛应用。F.Q.戈维亚著的《p进数导论(第2版)(英文版)》是介绍p进数理论的入门性教科书，与其它同类书相比，本书内容较为浅显易懂，适合那些无意成为专家但想对p进数有所了解的读者。

Introduction
1  Aperitif
  1.1  Hensers Analogy
  1.2  Solving Congruences Modulo pn
  1.3  Other Examples
2  Foundations
  2.1  Absolute Values on a Field
  2.2  Basic Properties
  2.3  Topology
  2.4  Algebra
3  p-adic Numbers
  3.1  Absolute Values on Q
  3.2  Completions
  3.3  Exploring Qp
  3.4  Hensel's Lemma
  3.5  Local and Global
4  Elementary Analysis in Qp
  4.1  Sequences and Series
  4.2  Functions, Continuity, Derivatives
  4.3  Power Series
  4.4  Functions Defined by Power Series
  4.5  Some Elementary Functions
  4.6  Interpolation
5  Vector Spaces and Field Extensions
  5.1  Normed Vector Spaces over Complete Valued Fields
  5.2  Finite-dimensional Normed Vector Spaces
  5.3  Finite Field Extensions
  5.4  Properties of Finite Extensions
  5.5  Analysis
  5.6  Example: Adjoining a p-th Root of Unity
  5.7  On to Cp
6  Analysis in Cp
  6.1  Almost Everything Extends
  6.2  Deeper Results on Polynomials and Power Series
  6.3  Entire Functions
  6.4  Newton Polygons
  6.5  Problems
A  Hints and Comments on the Problems
B  A Brief Glance at the Literature
  B.1  Texts
  B.2  Software
  B.3  Other Books
Bibliography
Index