ｐ進数：入門（第２版・テキスト） p-adic Numbers : An Introduction (Universitext) （2nd ed. 1997. Corr. 3rd printing）

Gouvea, Fernando Q.

Springer（2003/01発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 302 p.
• 商品コード 9783540629115

基本説明

An elementary introduction. This book can almost be viewed as an introduction to be read in preparation for reading these more advanced texts.

Full Description

There are numbers of all kindsp-adic numbers are less well known than the others, but they play a fundamental role in number theory and in other parts of mathematics. This elementary introduction offers a broad understanding of p-adic numbers.From the reviews: "It is perhaps the most suitable text for beginners, and I shall definitely recommend it to anyone who asks me what a p-adic number is." --THE MATHEMATICAL GAZETTE

Contents

1 Aperitif.- 1 Aperitif.- 1.1 Hensel's Analogy.- 1.2 Solving Congruences Modulopn.- 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 ?.- 3.2 Completions.- 3.3 Exploring ?p.- 3.4 Hensel's Lemma.- 3.5 Local and Global.- 4 Elementary Analysis in?p.- 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 ?.- 6 Analysis in?p.- 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.