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arXiv · 1106.5696

On the modified Selberg integral of the three-divisor function $d_3$

Giovanni Coppola
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Abstract

We prove a non-trivial result for the,say,modified Selberg integral $\modSel_3(N,h)$, of the divisor function $d_3(n):= \sum_{a}\sum_{b}\sum_{c, abc=n}1$; this integral is a slight modification of the corresponding Selberg integral, that gives the expected value of the function in short intervals. We get, in fact, $\modSel_3(N,h)\ll Nh^2L^2$, where $L:=\log N$; furthermore, as a byproduct, we obtain indications on the way in which it may be proved the weak sixth moment of the Riemann zeta function.(This was OLD abstract)

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Giovanni Coppola. 2012-09-21. On the modified Selberg integral of the three-divisor function $d_3$. https://arxiv.org/abs/1106.5696

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