Promotion And On Dhlehmer Problem On The Class Of Dedekind Sums And The Mean Value Formula

ABSTRACTAIastel' fIeg1.ee dissel'tatio1lOn a gelleralization of D.H.Lehmer's problem andon a mean value fOrmula of the sum analogous to Dedekind sums(DepartIllent of Llathell1atics, Northwest University, China)Del1g 1haping (Nun1ber Tlleory)directed by Zl1a11g 1VYnpel1gTl1is thesis totally has two sectiolls as follows:I. Let q IJe a11 odd illteger, k l2e an integer with k 2 3, 0 S a S 1 andtl > 0 be real nulnbers. YYfe defille one killd of number-theoretic ftllctionswllere Z' denotes tl1e sunlu1atiolls o\'er a sucll tllat (a, q) = '1, a'nd sj = l1 l j =Ql, 2,... l k. In tllis sectiolls, \ve use tlle estin1ates fOr genera'l I'loostermal1'ssunls alld tl1e lnetllods of trigollol11etric sun1 to obtain a sharp asymPtoticfOrmula for then1.II. For al1 odd illteger c alld all evell illteger d > 0, firstly defilled tlleanalogous Dedekilld suln S,(c, d), tllat isTlle n1aill PurPose of this sectioll is usillg tlle llleall value tl1eorel11 of tlle Diricll-let L-ftl11ctiol1s a11d t1le est'il11ates fOl' cllaractel' s[lll1s to st[1fl}' t1le as}fll1Ptoticprol,erties of tlle 111ean valuewllere l11, ll are Positive il1tegers, ((8, o) is tl1e Hurttitz zeta-ft1lctiol1.