Mean square of the error term in the asymmetric many dimensional divisor problem

الأصل · EN

Let =(a₁,a₂,,aₖ), where aⱼ (j=1,,k) are positive integers such that a₁ ≤ a₂ ≤ ≤ aₖ. Let d(;n)=∑n₁ᵃ¹ nₖᵃᵏ=n1 and Δ(;x) be the error term of the summatory function of d(;n). In this paper we show an asymptotic formula of the mean square of Δ(;x) under a certain condition. Furthermore, in the cases k=2 and 3, we give unconditional asymptotic formulas for these mean squares.