On the Selberg integral of the $k-$divisor function and the $2k-$th moment of the Riemann zeta function

Details On the Selberg integral of the $k-$divisor function and the $2k-$th moment of the Riemann zeta function On the Selberg integral of the $k-$divisor function and the $2k-$th moment of the Riemann zeta function

2009-07-31

arxiv.org/abs/0907.5561v1

Publications de l'Institut Math\'ematique (Beograd), 88(102) (2010), 99-110

Mathematics

Number Theory

This is (an expanded version of) my talk at JAXXVI (Plain TeX)

Scientific paper

We deeply appreciate the papers of Ivi\'c on the links between the $2k-$th moments of the Riemann zeta function and, say, $d_k$, the $k-$divisor function. More specifically, both the one bounding the $2k-$th moment with a simple average of correlations of the $d_k$ (Palanga 1996 Conference Proceedings) and the more recent (arXiv:0708.1601v2 to appear on JTNB), which bounds the Selberg integral of $d_k$ applying the $2k-$th moment of the zeta. Building on the former paper, we apply an elementary approach (based on arithmetic averages) in order to get information on the reverse link to the second work.

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