Tails $|t|>T$ of the smoothed Perron integral on $\sigma_0=1+1/\log X$ are $O(X\log X/(\varepsilon T))$

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Tails $|t|>T$ of the smoothed Perron integral on $\sigma_0=1+1/\log X$ are $O(X\log X/(\varepsilon T))$ · Prove2Me