Publications de l'Institut Mathématique, Nouvelle Série Vol. 88(102), pp. 99–111 (2010) 

ON THE SELBERG INTEGRAL OF THE $k$DIVISOR FUNCTION AND THE $2k$TH MOMENT OF THE RIEMANN ZETAFUNCTIONGiovanni CoppolaD.I.I.M.A., University of Salerno, 84084 Fisciano (SA), ItalyAbstract: In the literature one can find links between the $2k$th moment of the Riemann zetafunction 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 zetafunction. 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 zetafunction from the Selberg integral bounds involving $d_k(n)$. Classification (MSC2000): 11M06; 11N37 Full text of the article: (for faster download, first choose a mirror)
Electronic fulltext finalized on: 19 Nov 2010. This page was last modified: 6 Dec 2010.
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