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书名 p进数导论(第2版)(英文版)
分类 科学技术-自然科学-数学
作者 (美)F.Q.戈维亚
出版社 世界图书出版公司
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简介
内容推荐
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。
目录
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
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