Timeline for Distribution of square roots mod 1
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Feb 3, 2018 at 21:30 | comment | added | Igor Rivin | @Marty In particular, this argument shows that the error term cannot be improved to better than $O(\sqrt{n}).$ | |
| Feb 3, 2018 at 20:24 | comment | added | Marty | Oh - now I understand the "quarter-squares" bit. Makes sense! I've updated the question to use "Farey-binning" and bring out these spikes a bit more. | |
| Feb 3, 2018 at 17:05 | history | edited | Igor Rivin | CC BY-SA 3.0 |
made clearer
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| Feb 3, 2018 at 17:04 | comment | added | Igor Rivin | @Marty I was unclear above. Numbers of the form $(n^2-1)/4$ will give you the spike around $1/2$ - notice that half of all squares are equal to $1\mod 4,$ so there will be a spike at $\frac{1}{2}_-.$ | |
| Feb 3, 2018 at 4:37 | comment | added | Marty | I understand the source of the spike at zero (the squares, as you say). But I don't understand the "75 quarter-squares" bit. Do you have an explanation for the somewhat chaotic spiking around 0.5? | |
| Feb 3, 2018 at 0:05 | history | answered | Igor Rivin | CC BY-SA 3.0 |