Conrey, J. B.; Ghosh, A. A conjecture for the sixth power moment of the Riemann zeta-function. (English) Zbl 0920.11060 Int. Math. Res. Not. 1998, No. 15, 775-780 (1998). The authors give several heuristic arguments leading to the same conjecture, that \[ \int^T_0\biggl| \zeta\bigl( \tfrac 12+it\bigr) \biggr|^6dt\sim\tfrac{49}{9!} \left\{\prod_p \left(1-\tfrac 1p\right)^4 \left( 1+ \tfrac 4p+ \tfrac{1}{p^2} \right)\right\} T(\log T)^9. \] The unproven assumptions concern the extension of various mean-value estimates [J. B. Conrey and A. Ghosh, Proceedings of the Amalfi conference on analytic number theory, Maiori, 1989, Salerno, 35-59 (1992; Zbl 0792.11033)] beyond their known range of validity. Reviewer: D.R.Heath-Brown (Oxford) Cited in 4 ReviewsCited in 14 Documents MSC: 11M06 \(\zeta (s)\) and \(L(s, \chi)\) Keywords:Riemann Zeta-function; critical line; sixth power moment; conjecture; mean-value estimates PDF BibTeX XML Cite \textit{J. B. Conrey} and \textit{A. Ghosh}, Int. Math. Res. Not. 1998, No. 15, 775--780 (1998; Zbl 0920.11060) Full Text: DOI