I am finding the following first order estimate.
Question. As $y\rightarrow\infty$, $$\sum_{k=1}^{\infty}\frac{\log n}n\,\arctan\frac{y}n\,\, \sim\,\,\frac{\pi}4\log^2y.$$ Is it true?
asymptotic estimate for log-tan sum
T. Amdeberhan
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