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正版新书]P进数导论(美)F.Q.戈维亚 著9787519226121
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1.1 Hensels 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
3 p—adic Numbers
3.1 Absolute Values on Q
3.2 Completions
3.3 Exploring Qp
3.4 Hensels 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
5.6 Example: Adjoining a p—th R,oot 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
F.Q.戈维亚,是数论和算术几何领域的专家,尤其致力于研究模形式和伽罗瓦表示,也涉猎数学史的研究工作。
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