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How to estimate the integral of Riemann zeta function with error term trends to zero as T trends to infinity?

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RGM
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How to evaluateestimate the integral of Riemann zeta function?

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RGM
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How to evaluate the integral?

$\zeta(s)$ denotes the Riemann zeta function. For $T>0$ large enough $$\int_{T}^{2T}|\zeta(\frac{1}{3} + it) \ \zeta(\frac{2}{3} + it)|dt = \ ? $$