Baker A. - Introduction To p-adic Numbers and p-adic Analysis.pdf

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AnIntroductionto p -adicNumbersand p -adic
Analysis
A.J.Baker
[4/11/2002]
Department of Mathematics, University of Glasgow, Glasgow G12 8QW,
Scotland.
E-mailaddress : a.baker@maths.gla.ac.uk
URL : http://www.maths.gla.ac.uk/ » ajb
Contents
Introduction
1
Chapter1.Congruencesandmodularequations 3
Chapter2.The p -adicnormandthe p -adicnumbers 15
Chapter3.Someelementary p -adicanalysis 29
Chapter4.ThetopologyofQ p
33
Chapter5. p -adicalgebraicnumbertheory 45
Bibliography
51
Problems
53
ProblemSet1
53
ProblemSet2
54
ProblemSet3
55
ProblemSet4
56
ProblemSet5
57
ProblemSet6
58
1
Introduction
ThesenoteswerewrittenforafinalyearundergraduatecoursewhichranatManchester
Universityin1988/9andalsotaughtinlateryearsbyDrM.McCrudden.Irewrotethem
in2000tomakethemavailabletointerestedgraduatestudents.Theapproachtakenisvery
downtoearthandmakesfewassumptionsbeyondstandardundergraduateanalysisandalgebra.
Becauseofthisthecoursewasasselfcontainedaspossible,coveringbasicnumbertheoryand
analyticideaswhichwouldprobablybefamiliartomoreadvancedreaders.Theproblemsets
arebasedonthoseforproducedforthecourse.
IwouldliketothankJavierDiaz-Vargasforpointingoutnumerouserrors.
1

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