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Estimate of $\sum_{n=1}^x\exp(\pi i t/n)$ and $\sum_{n=-x}^x\exp(\pi i t/n)$?
I already asked this question here
https://math.stackexchange.com/questions/2005211/estimate-of-sum-n-1-infty-exp-pi-i-t-n/2005778#2005778
but I did not get a satisfying answer, so I put it here.
I ...
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