p-adic Numbers: An Introduction

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Springer Science & Business Media, May 22, 2003 - Mathematics - 306 pages
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In the course of their undergraduate careers, most mathematics majors see little beyond "standard mathematics:" basic real and complex analysis, ab stract algebra, some differential geometry, etc. There are few adventures in other territories, and few opportunities to visit some of the more exotic cor ners of mathematics. The goal of this book is to offer such an opportunity, by way of a visit to the p-adic universe. Such a visit offers a glimpse of a part of mathematics which is both important and fun, and which also is something of a meeting point between algebra and analysis. Over the last century, p-adic numbers and p-adic analysis have come to playa central role in modern number theory. This importance comes from the fact that they afford a natural and powerful language for talking about congruences between integers, and allow the use of methods borrowed from calculus and analysis for studying such problems. More recently, p-adic num bers have shown up in other areas of mathematics, and even in physics.
 

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Contents

II
7
IV
14
V
19
VI
23
VIII
29
IX
32
X
39
XI
43
XXV
134
XXVI
139
XXVII
143
XXVIII
158
XXIX
169
XXX
171
XXXI
176
XXXII
187

XIII
49
XIV
59
XV
69
XVI
77
XVII
87
XVIII
88
XIX
92
XX
95
XXI
102
XXII
111
XXIII
126
XXIV
133
XXXIV
191
XXXV
208
XXXVI
212
XXXVII
231
XXXVIII
235
XXXIX
291
XLI
292
XLII
293
XLIII
295
XLIV
299
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