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GH from MO
GH from MO
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Is it possible to get betteran upper bound for $$\int_{0}^{T}|\zeta (\sigma +it)dt$$ with $0<\sigma <1/2$better than $<<T^{1.5-\sigma}$?$\ll_\sigma T^{3/2-\sigma}$ for $$\int_{0}^{T}|\zeta (\sigma +it)|\,dt,\qquad 0<\sigma<1/2\,?$$

Is it possible to get better upper bound for $$\int_{0}^{T}|\zeta (\sigma +it)dt$$ with $0<\sigma <1/2$ than $<<T^{1.5-\sigma}$?

Is it possible to get an upper bound better than $\ll_\sigma T^{3/2-\sigma}$ for $$\int_{0}^{T}|\zeta (\sigma +it)|\,dt,\qquad 0<\sigma<1/2\,?$$

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user155294
user155294
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Moments of the Riemann zeta function

Is it possible to get better upper bound for $$\int_{0}^{T}|\zeta (\sigma +it)dt$$ with $0<\sigma <1/2$ than $<<T^{1.5-\sigma}$?