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This is a follow up question to this one.

It seems that results on moments of L-functions, that is, estimates for integrals of the form $$\int^{T}_1|\zeta(\sigma+it)|^{2k}dt$$ are typically for the incomplete L-function itself. Are there results for moments of completed L-functions, say, the completed Riemann zeta function?

If not, is the reason simply because the completed expression is more complicated than the incomplete one?

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    $\begingroup$ If you complete the zeta function, the Gamma factors will decay exponentially, so you will only pick up a contribution from small values of $t$, and this will be some constant for each $k$. $\endgroup$
    – Lucia
    Sep 30, 2015 at 17:33

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