On Higher-Power Moments of ${\Delta }_a(x)$ for $-1/2<a<0$

Yi Cai, Jinjiang Li, Yankun Sui +2

Let $-1/2<a<0$ be a fixed real number and \begin{equation*} Δ_{a}(x)=\sideset{}{'}\sum_{n\leq x} σ_a(n)-ζ(1-a)x-\frac{ζ(1+a)}{1+a}x^{1+a}+\frac{1}{2}ζ(-a). \end{equation*} In this…