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A conjecture for the sixth power moment of the Riemann zeta-function. (English) Zbl 0920.11060
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.

MSC:
11M06 \(\zeta (s)\) and \(L(s, \chi)\)
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