Timeline for Conjecture on irrational algebraic numbers
Current License: CC BY-SA 3.0
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Jul 6, 2014 at 16:58 | review | Low quality posts | |||
| Jul 6, 2014 at 17:30 | |||||
| Jul 6, 2014 at 12:20 | comment | added | Lev Borisov | Has this been done for $\sqrt D$ in arbitrary base? | |
| Jul 6, 2014 at 10:42 | comment | added | barak manos | Thanks. From the comments to my question, I realized that both section #2 and section #3 were pretty easy to answer (kind of dumb questions to begin with I suppose). @Geoff Robinson gave a good example answering section #3, similar to yours I think. | |
| Jul 6, 2014 at 10:16 | comment | added | P Vanchinathan | I did not know this was transcendental. Then this answers 3rd part of the question by OP. Thanks, Douglas Zare for such a detailed information and pointing out the reference. But I am still not able to figure out how to see that given number is the sum of the series you have described, also not able to see the connection to the Theta function paper you have cited. I'll think about it. | |
| Jul 6, 2014 at 9:49 | comment | added | Douglas Zare | For this to be relevant to the conjecture, the number you constructed would have to be algebraic, but it is transcendental because it is $2/9 - \sum_{n=1}^\infty (1/\sqrt{10})^{n(n+1)}$. The latter term is related to a theta function value and was proved to be transcendental. projecteuclid.org/… | |
| Jul 6, 2014 at 9:12 | history | answered | P Vanchinathan | CC BY-SA 3.0 |