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1、ANOTEONTHEFOURTHPOWERMOMENTOFTHERIEMANNZETA-FUNCTIONJ.B.ConreyAbstract.WegiveexplicitformulaeforallofthetermsintheasymptoticexpansionofthemeanfourthpoweroftheRiemannzeta-functiononthecriticalline.Heath-Brownhasevaluatedthe4thpowermomentoftheRiemannzeta-functiononthecriticallineviatheformulaZTT
2、47=8+I(T)=j(1=2+it)jdt=TPlog+O(T)2420wherePisa4thdegreepolynomial.HerewegiveanexplicitformulaforP.In44particular,weshowthatthecoecientsofPareinthe eld4000Q(;;;;(2);(2);(2))0123wherethe'sarethecoecientsintheLaurentexpansion1(s)=++(s
