On the basis of the Random Matrix Theory-model several interesting conjectures for the Riemann zeta-function were made during the recent past, in particular, asymptotic formulae for the 2kth continuous and discrete moments of the zeta-function on the critical line, $$frac{1}{T}intlimits_0^T {|zeta ( frac{1}{2} + it)|^{2k} dt} and frac{1}{{N(T)}}sumlimits_{0 gamma leqslant { m T}} {|zeta ( frac{1}{2} + i(gamma + frac{alpha }{L}))|^{2k} } $$, by Conrey, Keating et al. and Hughes, respectively. These conjectures are known to be true only for a few values of k and, even under assumption of the Riemann hypothesis, estimates of the expected order of magnitude are only proved for a limited range of k. We put the discrete moment for k = 1, 2 in relation with the corresponding continuous moment for the derivative of Hardya€?s Z-function. This leads to upper bounds for the discrete moments which are off the predicted order by a factor of log T.
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