Dedekind Sums And Promotion Of The Mean Value Formula Of Hardy And Promotion Mean Formula

ABSTRACTMaster degree dissertationOn the generalized mean value of Dedekind sumsandthe generalized mean value of Hardy sums(Department of Mathematics. Northwest University. China)Wang Yonghui (Number Theory)directed by Zhang ^VenpengThe main purpose of thesis is using the mean value theorem of the Dirichlet Lunctions to study the asymptotic property of the Dedekind sums and Hardy sums, and give two sharper asymptotic formulas.This paper is composed of two chapters. In chapter I, we give the 2mh generalized mean value of Dedekind sums. i.e. proving the mean value asymptotic formula in the form ofwhere p is l)rilTle. and m1(i = 1.2. . . . . k) are all even, and .S?ct^.p) denotes Dedekind sums. In chapter II. we give the 2m -th generalized mean value of Hardy sums. i.e. proving the mean value asymptotic formula in the form ofwhere p and m^{i 1.2. . . . k} are as above, and $(ct;.p) denotes Hardy sums.