Timeline for Sphere packing and modular forms in known dimensions (maybe 2)
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
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| Jun 30 at 6:05 | answer | added | Seewoo Lee | timeline score: 2 | |
| Sep 6, 2023 at 20:05 | comment | added | Breakfastisready | It's actually a wide open problem in this area to find these magic functions for the $A_2$ lattice in 2 dimensions. The methods don't generalize at all. Solving this problem would be huge. | |
| Sep 6, 2023 at 18:35 | comment | added | Will Sawin | The conjecture that a sharp bound can be obtained from the method is already in the Cohn-Elkies paper. "Based on numerical evidence and analogy with the kissing problem, we conjecture that [the linear programming method] can also be used to get sharp bounds in dimensions 2, 8, and 24." I don't know a reference that this isn't known yet soone than the Cohn survey, but it may be possible to find one just by looking around. | |
| Sep 6, 2023 at 18:28 | comment | added | Seewoo Lee | @SamHopkins You're right, just updated :) | |
| Sep 6, 2023 at 18:28 | comment | added | Seewoo Lee | @WillSawin Are there any reference about the point you mentioned? I just found that Cohn's survey article already mentioned about possibility on 2D case, but with no details. | |
| Sep 6, 2023 at 18:27 | history | edited | Seewoo Lee | CC BY-SA 4.0 |
added 41 characters in body
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| Sep 6, 2023 at 18:01 | comment | added | Will Sawin | It is not yet known how to construct a magic function in two dimensions. As far as I know it is believed that such a function exists, based on the known existence of functions proving close-to-optimal bounds, but the method of Viazovska based on interpolation does not seem to be able to produce it as there are not enough values to interpolate, and another method has not been found. | |
| Sep 6, 2023 at 17:43 | history | asked | Seewoo Lee | CC BY-SA 4.0 |