令ρ3(n)=∑n=|m|3-|l|3,(m,l)=1 1．本文研究了和式R3(x)=∑n≤xρ3(n)= A3x2／3+B3x1／2+E3(x),并且在黎曼假设下,得到E3(x)=0(x4／15+ε),从而进一步改进了前人的结果．

Letρ3(n)=∑n=|m|3-|l|3,(m,l)=1 1.In this paper we study the sum R3(x)=∑n≤xρ3(n)=A3x2／3+B3x1／2+E3(x), and we shall prove that if the Riemman Hypothesis (RH) is true, then E3(x)=O(x4/15+ε), which improves the previous result.