混合幂的除数和

摘要

令Sk(x)=∑ d(n21+n22+nk3),3≤k∈N.1≤n1,n2≤x1/21≤n3≤x1/k本文得到了渐近公式Sk(x) =A(k)x1+1/k log x + B(k)x1+1/k + O(x1+1/k-δ(k)+ε),这里A(k),B(k)是只与k有关的常数,δ(3)=5/42,δ(4)=1/16,δ(5)=1/40,并且当6≤k≤7时δ(k)=1/k2k-1,当k≥8时δ(k)=1/2k2(k-1).