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11N37 - Number theory :: Multiplicative number theory :: Asymptotic results on arithmetic functions

$\displaystyle x\log^2x=O\left(\sum_{n \le x} 2^{\Omega(n)} \right)$ owned by Wkbj79 $\displaystyle \sum_{n \le x} (\tau(n))^a=O_a(x(\log x)^{2^a-1})$ for $a \ge 0$ owned by Wkbj79 $\displaystyle \sum_{n \le x} y^{\Omega(n)}=O\left( \frac{x(\log x)^{y-1}}{2-y} \right)$ for $1 \le y<2$ owned by Wkbj79 $\displaystyle \sum_{n \le x} y^{\omega(n)}=O_y(x(\log x)^{y-1})$ for $y \ge 0$ owned by Wkbj79 analytic number theory owned by Wkbj79 asymptotic estimate owned by Wkbj79 asymptotic estimates for real-valued nonnegative multiplicative functions owned by Wkbj79 convolution method owned by Wkbj79 Dirichlet hyperbola method owned by Wkbj79 Wirsing condition owned by Wkbj79
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