Timeline for Structural description of Bohr sets in $\mathbb{Z}_N$
Current License: CC BY-SA 4.0
10 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Nov 23, 2023 at 14:45 | vote | accept | RFZ | ||
| Oct 8, 2023 at 6:25 | answer | added | Seva | timeline score: 3 | |
| Oct 7, 2023 at 23:59 | comment | added | Terry Tao | $\chi(x) \in e([-\delta,\delta])$ is equivalent to $|\chi(x)-1| \leq 2 \sin(\pi \delta)$, so one can prove a similar result after adjusting the value of $\delta$ appropriately. | |
| Oct 7, 2023 at 23:49 | comment | added | RFZ | @TerryTao, I agree that he uses a definition which is quite different from the one I provided. However, I am wondering if it is possible to prove the same type of result with my definition. I have been trying for a few days, but it has not worked out yet. | |
| Oct 7, 2023 at 23:44 | comment | added | Terry Tao | Your definition of a Bohr set is not quite the one that Gowers uses (see youtu.be/… ); he uses the condition $\chi(x) \in e([-\delta,\delta])$ rather than $|\chi(x)-1| \leq \delta$. | |
| Oct 7, 2023 at 20:18 | comment | added | RFZ | @Seva, Interesting! I asked this question because I am watching the lecture series 'Introduction to Additive Combinatorics' by Tim Gowers, in which he proved the lemma I was inquiring about. That is why I asked this question. Here is the link: youtube.com/… | |
| Oct 7, 2023 at 19:27 | comment | added | Seva | Not that I've checked it carefully, but I think the map is not surjective: in fact, $\mathrm{Bohr}(\Gamma,\delta)$ is Freiman-isomorphic to order $r$ to a subset of $\Lambda\cap[-\delta N/4,\delta N/4]^k$. | |
| Oct 7, 2023 at 18:42 | comment | added | RFZ | @NickS, yes exactly. | |
| Oct 7, 2023 at 18:15 | comment | added | Nick S | What is $\mathbb Z_{N}$? Is it $\mathbb Z/N \mathbb Z$ ? | |
| Oct 7, 2023 at 18:05 | history | asked | RFZ | CC BY-SA 4.0 |