Timeline for Is there a matrix C so that the trace of C^n is dense in R?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 10, 2010 at 18:50 | vote | accept | Hej | ||
| Feb 12, 2010 at 1:41 | comment | added | George Lowther | Bjorn - it still gets a little messy choosing the binary digits correctly. Your answer seems pretty good to me and, as it's way past my bedtime now, I'll leave it at that. | |
| Feb 12, 2010 at 1:39 | comment | added | George Lowther | I don't know if picking a z at random like that will work but, according to my response, the chances of it working are zero:) | |
| Feb 12, 2010 at 1:17 | comment | added | Victor Miller | Bjorn, very nice! I wonder if it's possible to describe a $z$ that works more explicitly? We know that $\theta = \arg(z)/2\pi$ must be irrational, so it would be interesting to start with a particular case, say $\theta = \sqrt{2}-1$, and see if we can find a value for $|z|$ that works. | |
| Feb 12, 2010 at 1:14 | comment | added | Bjorn Poonen | Yes. In fact, your approach has the advantage that it gives a more explicit theta. Sorry for posting my solution just as you were about to post yours. | |
| Feb 12, 2010 at 0:48 | comment | added | George Lowther | Ok, cool. I was about to write something similar as per my comment above, using the binary expansion of theta/pi using the idea behind the construction of the Liouville constant. Think it boils down to the same basic idea as this answer though. | |
| Feb 12, 2010 at 0:45 | history | edited | Bjorn Poonen | CC BY-SA 2.5 |
corrected the justification for the existence of I_j
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| Feb 12, 2010 at 0:39 | history | answered | Bjorn Poonen | CC BY-SA 2.5 |