Timeline for $\limsup_{n\rightarrow \infty, n\in\mathbb{N}} \sin(n)^{n^x}$ for various $x$
Current License: CC BY-SA 4.0
11 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2023 at 17:56 | comment | added | Iosif Pinelis | @SungjinKim : Yes, you are right. | |
| Aug 3, 2023 at 17:04 | comment | added | Sungjin Kim | By the same argument with specifying the constant in $O(1/q^2)$, we may obtain a positive lower bound of $f(2)$. | |
| Jul 16, 2023 at 16:22 | comment | added | ninepointcircle | Thanks a lot for the answer! I found this problem on one of the t-shirts that were dustributed in a math competition about 10 years ago. Unfortunately, I don't have an answer to the second part of the problem either. | |
| Jul 14, 2023 at 16:13 | comment | added | Iosif Pinelis | @GeraldEdgar : You are quite right. For $x=2$, it seems we have to deal with Diophantine approximation to $\pi$, rather than that to a arbitrary irrational number. This seems to be an open problem. | |
| Jul 14, 2023 at 16:13 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jul 14, 2023 at 15:43 | comment | added | Gerald Edgar | Same argument for $1\le x < 2$. But $x=2$ is on the border, this computation does not answer that case. | |
| Jul 14, 2023 at 15:37 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jul 14, 2023 at 15:28 | history | undeleted | Iosif Pinelis | ||
| Jul 14, 2023 at 15:28 | history | edited | Iosif Pinelis | CC BY-SA 4.0 |
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| Jul 14, 2023 at 14:58 | history | deleted | Iosif Pinelis | via Vote | |
| Jul 14, 2023 at 14:56 | history | answered | Iosif Pinelis | CC BY-SA 4.0 |