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内容简介
thegeneralaimofthisbookistoprovideamodernapproachtonumbertheorythroughablendingofcomplementaryalgebraicandanalyticperspectives,emphasizingharmonicanalysisontopologicalgroups.themoreparticulargoalistocoverjohntate’svisionarythesis,givingvirtuallyallofthenecessaryanalyticdetailsandtopologicalpreliminaries---technicalprerequisitesthatareoftenforeigntothetypical,morealgebraicallyinclinednumbertheorist.whilemostoftheexistingtreatmentsoftate’sthesisaresomewhatterseandlessthancomplete,theauthors’intentistobemoreleisurely,morecomprehensive,andmorecomprehensible.thetextaddressesstudentswhohavetakenayearofgraduate-levelcoursesinalgebra,analysis,andtopology.whilethechoiceofobjectsandmethodsisnaturallyguidedbyspecificmathematicalgoals,theapproachisbynomeansnarrow.infact,thesubjectmatterathandisgermanenotonlytobuddingnumbertheorists,butalsotostudentsofharmonicanalysisortherepresentationtheoryofliegroups.moreover,theworkshouldbeagoodreferenceforworkingmathematiciansinterestedinanyofthesefields.specifictopicsinclude:topologicalgroups,representationtheory,dualityforlocallycompactabeliangroups,thestructureofarithmeticfields,adelesandideles,anintroductiontoclassfieldtheory,andtate’sthesisandapplications.
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