Timeline for Bounds on imaginary parts of partial Kloosterman sums?
Current License: CC BY-SA 3.0
7 events
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| Jun 22, 2022 at 7:16 | history | edited | CommunityBot |
replaced http://front.math.ucdavis.edu/ with https://arxiv.org/abs/
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| Nov 29, 2014 at 4:54 | vote | accept | Kirill | ||
| Nov 29, 2014 at 4:54 | comment | added | Kirill | Thank you for the answer and the link; I managed to plot them here. | |
| Nov 29, 2014 at 3:23 | comment | added | Noam D. Elkies | Yes, but I expect that this bound would greatly overestimate the actual first occurrence. | |
| Nov 28, 2014 at 22:14 | comment | added | Will Sawin | @NoamD.Elkies One could extract from the methods of the paper you could get an explicif lower bound on an explicit lower bound for the first p where it gets larger than a given constant so you could see when it happens. | |
| Nov 28, 2014 at 6:09 | comment | added | Noam D. Elkies | If I computed right, the first case of $\left|{\rm Im} \, S_p(a,m)\right| > \sqrt p$ is ${\rm Im} \, S_{53}(24,14) = 7.2877\ldots = 1.0010\ldots \sqrt{53}$, and there is no case of $\left|{\rm Im} \, S_p(a,m)\right| > \sqrt{2p}$ for $p<2000$, though the ratios are inching closer to $\sqrt 2$, and are bound to exceed $\sqrt 2$ eventually. | |
| Nov 28, 2014 at 5:54 | history | answered | Denis Chaperon de Lauzières | CC BY-SA 3.0 |