From the reviews: "This is a well-written introduction to the world of p-adic numbers. The reader is led into the rich structure of the fields Qp and Cp in a beautiful balance between analytic and algebraic aspects. The overall conclusion is simple: an extraordinarily nice manner to introduce the uninitiated to the subject. Not only giving the background necessary to pursue the matter, but doing it in such a way that a healthy 'hands-on experience'is generated in the process." Mededelingen van het wiskundig genootschap "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
Author(s): Fernando Quadros Gouvea
Series: Universitext
Edition: 2nd
Publisher: Springer
Year: 1997
Language: English
Pages: 310
Contents......Page all_25567_to_00310.cpc0007.djvu
Introduction......Page all_25567_to_00310.cpc0009.djvu
1.1 Hensel's Analogy......Page all_25567_to_00310.cpc0015.djvu
1.2 Solving Congruences Modulo p^n......Page all_25567_to_00310.cpc0022.djvu
1.3 Other Examples......Page all_25567_to_00310.cpc0027.djvu
2.1 Absolute Values on a Field......Page all_25567_to_00310.cpc0031.djvu
2.2 Basic Properties......Page all_25567_to_00310.cpc0037.djvu
2.3 Topology......Page all_25567_to_00310.cpc0040.djvu
2.4 Algebra......Page all_25567_to_00310.cpc0047.djvu
3.1 Absolute Values on Q......Page all_25567_to_00310.cpc0051.djvu
3.2 Completions......Page all_25567_to_00310.cpc0057.djvu
3.3 Exploring Q_p......Page all_25567_to_00310.cpc0067.djvu
3.4 Hensel's Lemma......Page all_25567_to_00310.cpc0077.djvu
3.5 Local and Global......Page all_25567_to_00310.cpc0085.djvu
4 Elementary Analysis in Q_p......Page all_25567_to_00310.cpc0095.djvu
4.1 Sequences and Series......Page all_25567_to_00310.cpc0096.djvu
4.2 Functions, Continuity, Derivatives......Page all_25567_to_00310.cpc0100.djvu
4.3 Power Series......Page all_25567_to_00310.cpc0103.djvu
4.4 Functions Defined by Power Series......Page all_25567_to_00310.cpc0110.djvu
4.5 Some Elementary Functions......Page all_25567_to_00310.cpc0119.djvu
4.6 Interpolation......Page all_25567_to_00310.cpc0134.djvu
5 Vector Spaces and Field Extensions......Page all_25567_to_00310.cpc0141.djvu
5.1 Normed Vector Spaces over Complete Valued Fields......Page all_25567_to_00310.cpc0142.djvu
5.2 Finite-dimensional Normed Vector Spaces......Page all_25567_to_00310.cpc0147.djvu
5.3 Finite Field Extensions......Page all_25567_to_00310.cpc0151.djvu
5.4 Properties of Finite Extensions......Page all_25567_to_00310.cpc0166.djvu
5.5 Analysis......Page all_25567_to_00310.cpc0177.djvu
5.6 Example: Adjoining a p-th Root of Unity......Page all_25567_to_00310.cpc0179.djvu
5.7 On to C_p......Page all_25567_to_00310.cpc0184.djvu
6.1 Almost Everything Extends......Page all_25567_to_00310.cpc0195.djvu
6.2 Deeper Results on Polynomials and Power Series......Page all_25567_to_00310.cpc0199.djvu
6.3 Entire Functions......Page all_25567_to_00310.cpc0216.djvu
6.4 Newton Polygons......Page all_25567_to_00310.cpc0220.djvu
6.5 Problems......Page all_25567_to_00310.cpc0239.djvu
A Hints and Comments on the Problems......Page all_25567_to_00310.cpc0243.djvu
B.1 Texts......Page all_25567_to_00310.cpc0299.djvu
B.2 Software......Page all_25567_to_00310.cpc0300.djvu
B.3 Other Books......Page all_25567_to_00310.cpc0301.djvu
Bibliography......Page all_25567_to_00310.cpc0303.djvu
Index......Page all_25567_to_00310.cpc0307.djvu
