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Timeline for Distribution of square roots mod 1

Current License: CC BY-SA 3.0

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Feb 3, 2018 at 21:40 vote accept Marty
Feb 3, 2018 at 20:56 history edited Lucia CC BY-SA 3.0
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Feb 3, 2018 at 7:03 comment added Marty Thanks for the edits and explanations. Maybe I can figure out the spikes from that formula for the number of $n$ with $\{ \sqrt{n} \} \in (\alpha, \beta)$.
Feb 3, 2018 at 6:10 history edited Lucia CC BY-SA 3.0
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Feb 3, 2018 at 4:49 comment added Marty Excellent! I think this answers Question #1. I'm going to leave the question open for a little while to see if anyone answers (parts of) Question #2. In the meantime, I wonder about your answer -- can such estimates of exponential sums explain the visible difference between the flatness of the $\sqrt{n}$ and the noise of the $\sqrt{p}$ distributions?
Feb 2, 2018 at 23:45 history answered Lucia CC BY-SA 3.0