Timeline for Is pi = log_a(b) for some integers a, b > 1?
Current License: CC BY-SA 3.0
8 events
| when toggle format | what | by | license | comment | |
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| May 22, 2017 at 1:58 | comment | added | Sungjin Kim | @BalarkaSen Any nontrivial linear combinations of $\{\pi, \log 2, \log 3, \log 5, \ldots\}$ with algebraic coefficients is transcendental. This follows from Baker's theorem. | |
| Jul 10, 2014 at 14:46 | comment | added | Balarka Sen | I am not sure if in general we currently have anything about $\pi$ being or not being in $\mathcal{EL}$ but some developments have been made in "Adhikari, S. D.; Saradha, N.; Shorey, T. N.; Tijdeman, R. Transcendental infinite sums. Indag. Math. (N.S.) 12 (2001), no. 1, 1-14.". The sum has been evaluated in here, so what they really proved is that $\pi/\sqrt{3} + \log(3)$ is transcendental. I think this is the best we have for now. | |
| Jan 12, 2013 at 16:32 | vote | accept | Stefan Kohl♦ | ||
| Jan 11, 2013 at 22:13 | comment | added | Stefan Kohl♦ | @Timothy: Good answer! -- I will wait some time whether someone can still tell some more, and if not, I will accept your answer. | |
| Jan 11, 2013 at 19:42 | comment | added | Timothy Chow | Tom, good catch! | |
| Jan 11, 2013 at 19:05 | comment | added | Tom Church | Dear Timothy, I removed two words from your excellent answer because I feared they could be misinterpreted. If you don't agree with their removal, I apologize, and you should feel free to add them back in. Best wishes, Tom | |
| Jan 11, 2013 at 19:03 | history | edited | Tom Church | CC BY-SA 3.0 |
removed "and intelligent"
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| Jan 11, 2013 at 17:49 | history | answered | Timothy Chow | CC BY-SA 3.0 |