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P-adic numbers : an introduction

P-adic numbers : an introduction (Loan 6 times)

Material type
단행본
Personal Author
Gouv?a, Fernando Q. (Fernando Quadros)
Title Statement
P-adic numbers : an introduction / Fernando Q. Gouv?a.
Publication, Distribution, etc
Berlin ;   New York :   Springer-Verlag,   c1993.  
Physical Medium
vi, 282 p. : ill. ; 24 cm.
Series Statement
Universitext
ISBN
3540568441 (Berlin : acid-free paper) 0387568441 (New York : acid-free paper)
Bibliography, Etc. Note
Includes bibliographical references (p. [277]-278) and index.
Subject Added Entry-Topical Term
Nombres p-adiques. p-adic numbers.
000 00839camuuu200253 a 4500
001 000000220972
005 19951110145754.0
008 930610s1993 gw a b 001 0 eng
010 ▼a 93025593
020 ▼a 3540568441 (Berlin : acid-free paper)
020 ▼a 0387568441 (New York : acid-free paper)
040 ▼a DLC ▼c DLC ▼d FPU
049 ▼a ACCL ▼l 111055018
050 0 0 ▼a QA241 ▼b .G64 1993
082 0 0 ▼a 512/.74 ▼2 20
090 ▼a 512.74 ▼b G719p
100 1 ▼a Gouv?a, Fernando Q. ▼q (Fernando Quadros)
245 1 0 ▼a P-adic numbers : ▼b an introduction / ▼c Fernando Q. Gouv?a.
260 ▼a Berlin ; ▼a New York : ▼b Springer-Verlag, ▼c c1993.
300 ▼a vi, 282 p. : ▼b ill. ; ▼c 24 cm.
490 0 ▼a Universitext
504 ▼a Includes bibliographical references (p. [277]-278) and index.
650 7 ▼a Nombres p-adiques. ▼2 ram
650 0 ▼a p-adic numbers.

Holdings Information

No. Location Call Number Accession No. Availability Due Date Make a Reservation Service
No. 1 Location Main Library/Western Books/ Call Number 512.74 G719p Accession No. 111055018 Availability Available Due Date Make a Reservation Service B M

Contents information

Table of Contents


CONTENTS
Introduction = 1
1 Ap e ´ ritif = 5
  1.1 Hensel's Analogy = 5
  1.2 Solving Congruences Modulo pn = 12
  1.3 Other Examples = 17
2 Foundations = 21
  2.1 Absolute Values on a Field = 21
  2.2 Basic Properties = 27
  2.3 Topology = 29
  2.4 Algebra = 37
3 p-adic Numbers = 41
  3.1 Absolute Values on Q = 41
  3.2 Completions = 47
  3.3 Exploring Qp = 58
  3.4 Hensel's Lemma = 67
  3.5 Local and Global = 75
4 Elementary Analysis in Qp = 85
  4.1 Sequences and Series = 86
  4.2 Power Series = 88
  4.3 Some Elementary Functions = 97
  4.4 Interpolation = 109
5 Vector Spaces and Field Extensions = 117
  5.1 Normed Vector Spaces over Complete Valued Field = 118
  5.2 Finite-dimensional Normed Vector Spaces = 123
  5.3 Finite Field Extensions = 127
  5.4 Properties of Finite Extensions = 142
  5.5 Analysis = 153
  5.6 Example: Adjoining a p-th Root of Unity = 155
  5.7 On to Cp = 161
6 Analysis in Cp = 171
  6.1 Almost Everything Extends = 171
  6.2 Derivatives = 175
  6.3 Deeper Results on Polynomials and Power Series = 177
  6.4 Entire Functions = 195
  6.5 Newton Polygons = 199
  6.6 Problems = 217
A. Hints and Comments on the Problems = 221
B. A Brief Glance at the Literature = 273
  B.1 Texts = 273
  B.2 Software = 274
  B.3 Other books = 275
Bibliography = 277
Index = 279

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