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Divisor function

{title2=$\sum_{n\le X}d(n)^2\ll X\log^3(2X)$}

The <divisor function> satisfies $\sum_{n\le X}d(n)^2\ll X\log^3(2X)$. <Partial summation> consequently gives $\sum_{n\le X}d(n)^2/n\ll\log^4(2X)$.

Divisor-square summatory bound

Fourth moment of the Riemann zeta function

Past exam of the mathematics course of the University of Cambridge / 2016 / iii / Paper 124 / 4 / c / Solution

Divisor-square summatory bound ( $\sum_{n \leq X} d (n)^{2} ≪ X lo g^{3} (2 X)$ )

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Divisor-square summatory bound (∑n≤X​d(n)2≪Xlog3(2X))

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Divisor-square summatory bound ( $\sum_{n \leq X} d (n)^{2} ≪ X lo g^{3} (2 X)$ )

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