Timeline for One question on linear combinations of roots of unity
Current License: CC BY-SA 4.0
30 events
| when toggle format | what | by | license | comment | |
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| S Jan 2, 2023 at 23:02 | history | bounty ended | CommunityBot | ||
| S Jan 2, 2023 at 23:02 | history | notice removed | CommunityBot | ||
| Dec 29, 2022 at 1:16 | history | edited | user369335 |
edited tags
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| S Dec 27, 2022 at 2:23 | vote | accept | user369335 | ||
| Dec 27, 2022 at 2:22 | vote | accept | user369335 | ||
| S Dec 27, 2022 at 2:23 | |||||
| Dec 26, 2022 at 22:06 | answer | added | YCor | timeline score: 7 | |
| S Dec 25, 2022 at 21:37 | history | bounty started | user369335 | ||
| S Dec 25, 2022 at 21:37 | history | notice added | user369335 | Canonical answer required | |
| Dec 25, 2022 at 21:32 | history | edited | user369335 | CC BY-SA 4.0 |
About my motivations
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| Dec 25, 2022 at 20:17 | comment | added | Max Lonysa Muller | @user369335 I'm curious: do you have a certain motivation for this question? | |
| Dec 24, 2022 at 21:38 | history | edited | user369335 | CC BY-SA 4.0 |
Update two tables
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| Dec 24, 2022 at 19:04 | history | edited | user369335 | CC BY-SA 4.0 |
added 345 characters in body
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| Dec 24, 2022 at 18:46 | comment | added | user369335 | @PeterTaylor I think $x_i \in [-1,1]$ is more difficult than $x_i = \pm 1$, so I made this change. If the basic case is solved, I will focus on the more general cases. Any comment for this problem and its variations will be appreciated. | |
| Dec 24, 2022 at 15:26 | comment | added | Peter Taylor | Is the change from $x_i \in [-1,1]$ to $x_i\in \mathbb{Z}, x_i^2 = 1$ intended as $x_i = \pm 1$, or is there a typo somewhere? | |
| Dec 24, 2022 at 3:24 | history | edited | user369335 | CC BY-SA 4.0 |
Update the table
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| Dec 23, 2022 at 23:10 | history | edited | user369335 | CC BY-SA 4.0 |
Follow Alex M.'s advice
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| Dec 23, 2022 at 22:49 | comment | added | user369335 | It is much faster now :) Thank you. @LSpice | |
| Dec 23, 2022 at 22:41 | comment | added | LSpice | Your tables took a very long time to render for me because each number was rendered as its own formula. Removing them from math mode seems to preserve all semantic information and make the page load much more quickly, so I did so. I hope that is all right. | |
| Dec 23, 2022 at 22:41 | history | edited | LSpice | CC BY-SA 4.0 |
De-math-moding numbers
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| Dec 23, 2022 at 22:15 | answer | added | user369335 | timeline score: 3 | |
| Dec 23, 2022 at 21:12 | comment | added | user369335 | This construction is valid, but it seems that $z*conj(z)$ is always $p+1$. | |
| Dec 23, 2022 at 20:18 | comment | added | YCor | For prime $p=4n-1$, up to translation, complex conjugation and complementation, the function giving rise to integral norm seems to to be the one mapping a nonzero square mod $p$ to $1$ and nonsquares and zero mod $p$ to $-1$. | |
| Dec 23, 2022 at 1:11 | history | edited | user369335 | CC BY-SA 4.0 |
Add the further detail
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| Dec 22, 2022 at 21:51 | comment | added | user369335 | @paulgarrett Yes! Thank you for your comment. | |
| Dec 22, 2022 at 21:34 | history | edited | user369335 |
edited tags
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| Dec 22, 2022 at 21:25 | comment | added | paul garrett | Although this also has strong "harmonic analysis" aspects, I suspect that it would be easier to give structural answers when $n$ is prime $p$, perhaps especially when $p=2q+1$ with prime $q$... for Galois-theory reasons. This would be a quite slim slice of the whole space of examples... but/and would it be of interest to you? | |
| Dec 22, 2022 at 21:19 | history | edited | user369335 | CC BY-SA 4.0 |
Add the computational result
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| Dec 22, 2022 at 16:19 | comment | added | Antoine Labelle | Do the solutions for small n suggest any pattern? | |
| Dec 22, 2022 at 1:19 | history | edited | user369335 | CC BY-SA 4.0 |
added 42 characters in body
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| Dec 21, 2022 at 22:34 | history | asked | user369335 | CC BY-SA 4.0 |