Timeline for Show that $(\sum_{k=1}^{n}x_{k}\cos{k})^2+(\sum_{k=1}^{n}x_{k}\sin{k})^2\le (2+\frac{n}{4})\sum_{k=1}^{n}x^2_{k}$
Current License: CC BY-SA 4.0
9 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Mar 19, 2020 at 10:57 | comment | added | Ivan Meir | @FedorPetrov I have added a stronger result but conditional on the irrationality measure of $\pi$ being less than 3. | |
| Mar 18, 2020 at 19:30 | history | edited | Ivan Meir | CC BY-SA 4.0 |
Minor formatting change
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| Mar 15, 2020 at 18:42 | comment | added | Lucia | This was already noted in the linked question (Bounding a Fourier ...) | |
| Mar 15, 2020 at 18:40 | history | edited | Ivan Meir | CC BY-SA 4.0 |
Updated first sentence based on Fedor Petrov's comment.
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| Mar 15, 2020 at 15:14 | comment | added | Ivan Meir | @FedorPetrov Thank you for clarifying - yes I understand - you are absolutely right we don't get the OP's inequality, not quite anyway. I will update my answer to reflect your comment. I do have a more complicated method that I think will give the result precisely for large n and I'll post that if I have time later. | |
| Mar 15, 2020 at 13:11 | comment | added | Fedor Petrov | It is not proved for large $n$, what you prove is $n/4+o(n)$ which is a weaker upper bound than $n/4+2$. | |
| Mar 15, 2020 at 9:54 | comment | added | Ivan Meir | @FedorPetrov Do you mean because it's only proved for sufficiently large n? | |
| Mar 15, 2020 at 7:25 | comment | added | Fedor Petrov | it is weaker than needed | |
| Mar 15, 2020 at 3:54 | history | answered | Ivan Meir | CC BY-SA 4.0 |