关于DEDEKIND和与原特征的混合均值

On the hybrid mean value of Dedekind sums and primitive characters

对正整数K和任意整数H,DEDEKIND和定义为:S(H,K)=SUM FORM A=1 TO K((A/K))((AH/K)),其中 (H,K)=1 且利用DIRICHLET L-函数的均值定理研究了DEDEKIND和与原特征Χ*的混合均值SUM FROM H=1 TO K Χ*(H) |S(H,K)|2,并给出了一个有趣的渐近公式．

For any integers k 〉0 and h, the Dedekind sums are defined as follows： S（h,k）=∑（（a/k））（（ah/k）） where （h,k） =1 and （（x）） ={x-[x]-1/2, if x is not an integer; 0 , if x is an integer. Using the mean value theorem of Dirichlet L - functions, the hybrid mean value of Dedekind sums and primitive characters ∑X^＊（h）｜S（h,k）｜^2, is studied and an interesting asymptotic formula is given