.

0 (hodnocen0 x )

(4) Půjčeno:4x 

BK

2nd ed.

Berlin : Springer, c1997

vi,298 s.

ISBN 3-540-62911-4 (brož.)

Universitext

Obsahuje rejstřík.

Bibliografie: s. 291-293.

P-adic (čísla) - učebnice vysokošk.

000078569

Introduction // 1 Aperitif // 1.1 Hensels Analogy // 12 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 // 23 // 23 // 29 // 32 // 39 // 3 p-adic Numbers 43 // 3.1 Absolute Values on Q 43 // 3.2 Completions 49 // 3.3 Exploring Qp 59 // 3.4 Hensels Lemma 69 // 3.5 Local and Global 77 // 4 Elementary Analysis in Qp 87 // 4.1 Sequences and Series 88 // 4.2 Functions, Continuity, Derivatives 92 // 4.3 Power Series 95 // 4.4 Functions Defined by Power Series 102 // 4.5 Some Elementary Functions Ill // 4.6 Interpolation 126 // 5 Vector Spaces and Field Extensions 133 // 5.1 Normed Vector Spaces over Complete Valued Fields 134 // 5.2 Finite-dimensional Normed Vector Spaces 139 // 5.3 Finite Field Extensions 143 // 5.4 Properties of Finite Extensions 158 // 5.5 Analysis 169 // 5.6 Example: Adjoining a p-th Root of Unity 171 // 5.7 On to Cp 176 // vi 0 Contents // 6 Analysis in Cp 187 // 6.1 Almost Everything Extends 187 // 6.2 Deeper Results on Polynomials and Power Series 19i // 6.3 Entire Functions 208 // 6.4 Newton Polygons 212 // 6.5 Problems 231 // A Hints and Comments on the Problems 235 // ? A Brief Glance at the Literature 291 // B.l Texts 291 // B.2 Software 292 // B.3 Other Books 293 // Bibliography 295 // Index // 299