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References to 'convolution method'
1. $\displaystyle x\log^2x=O\left(\sum_{n \le x} 2^{\Omega(n)} \right)$ by Wkbj79
2. $\displaystyle \sum_{n \le x} y^{\Omega(n)}=O\left( \frac{x(\log x)^{y-1}}{2-y} \right)$ for $1 \le y<2$ by Wkbj79
3. analytic number theory by Wkbj79
4. asymptotic estimate by Wkbj79