Timeline for Is there an explicit example of a complex number which is not a period?
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| Apr 6, 2010 at 8:39 | comment | added | Wadim Zudilin | Although it is clearly a right way to provide an example of non-period, by showing a certain nice approximativity of periods (and this was exactly Liouville's trick in 1844), I wonder whether the proofs are correct. I'll make a serious look only after the results appear in a serious journal. Sorry for my sceptisism. | |
| Apr 6, 2010 at 1:04 | comment | added | Gjergji Zaimi | @Douglas Zare: I'm guessing the article above is one of the first to give any sort of qualitative property of periods. And I think it makes sense that as an application he constructed a computable number that is "non-elementary", even though Chaitin's constant could have produced a faster counter example. This would probably be the difference of what M. Waldschmidt calls analog of Liouville vs. analog of Hermite in swc.math.arizona.edu/aws/08/slides/08WaldschmidtSlides5.pdf (slide no. 31) :) | |
| Apr 6, 2010 at 0:44 | comment | added | Gjergji Zaimi | Tent and Ziegler also have a proof of Yoshinaga's theorem. arxiv.org/abs/0903.1384 | |
| Apr 6, 2010 at 0:32 | comment | added | Douglas Zare | I haven't followed the details of that paper yet, but I would expect that it's simpler to prove that Chaitin's constant $\Omega$ is not a period, although computable numbers may be viewed as more explicit than $\Omega$. | |
| Apr 5, 2010 at 23:50 | history | answered | Gjergji Zaimi | CC BY-SA 2.5 |