Geodesic
On the Selberg Integral of the $k$-divisor Function and the $2k$-th Moment of the Riemann Zeta-function
Publications de l'Institut Mathématique, _N_S_88 (2010) no. 102, p. 99

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In the literature one can find links between the $2k$-th moment of the Riemann zeta-function and averages involving $d_k(n)$, the divisor function generated by $\zeta^k(s)$. There are, in fact, two bounds: one for the $2k$-th moment of $\zeta(s)$ coming from a simple average of correlations of the $d_k$; and the other, which is a more recent approach, for the Selberg integral involving $d_k(n)$, applying known bounds for the $2k$-th moment of the zeta-function. Building on the former work, we apply an elementary approach (based on arithmetic averages) in order to get the reverse link to the second work; i.e., we obtain (conditional) bounds for the $2k$-th moment of the zeta-function from the Selberg integral bounds involving $d_k(n)$.
Classification : 11M06 11N37 
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     author = {Giovanni Coppola},
     title = {On the {Selberg} {Integral} of the $k$-divisor {Function} and the $2k$-th {Moment} of the {Riemann} {Zeta-function}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {99 },
     publisher = {mathdoc},
     volume = {_N_S_88},
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     year = {2010},
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     url = {http://geodesic.mathdoc.fr/item/PIM_2010_N_S_88_102_a6/}
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Giovanni Coppola. On the Selberg Integral of the $k$-divisor Function and the $2k$-th Moment of the Riemann Zeta-function. Publications de l'Institut Mathématique, _N_S_88 (2010) no. 102, p. 99 . http://geodesic.mathdoc.fr/item/PIM_2010_N_S_88_102_a6/