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

preprint2012arXivOpen access

We give a new non-trivial upper bound for the Selberg integral of the three-divisor function $d_3(n)$ . Our method applies our recent conjecture together with Laporta, for the modified Selberg integral of $d_3(n)$ , and a kind of modified Gallagher Lemma for the exponential sums.

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

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On the Selberg integral of the three-divisor function d3d_3d3​

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