Coppola, Giovanni On the Selberg integral of the \(k\)-divisor function and the \(2k\)-th moment of the Riemann zeta-function. (English) Zbl 1337.11056 Publ. Inst. Math., Nouv. Sér. 88(102), 99-110 (2010). Summary: 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 \(d_k(n)\). Cited in 2 ReviewsCited in 3 Documents MSC: 11M06 \(\zeta (s)\) and \(L(s, \chi)\) 11N37 Asymptotic results on arithmetic functions Keywords:Selberg integral; moments; Riemann zeta-function PDFBibTeX XMLCite \textit{G. Coppola}, Publ. Inst. Math., Nouv. Sér. 88(102), 99--110 (2010; Zbl 1337.11056) Full Text: DOI arXiv EMIS