Timeline for A closure operation on subsets of ${\Bbb Z}[x]$
Current License: CC BY-SA 3.0
5 events
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| Feb 21, 2012 at 23:01 | comment | added | David Feldman | @Jérôme A special case of your suggestion amounts to finding the degree 1 polynomials in "closure," which just means finding the points x lying in the topological closure of all the roots. Off the top of my head I guess that to identify such $x$ one might consider whether the set $\{ f(x)/f'(x) | f \in S\}$ has $0$ as a limit point, or at least something like that. | |
| Feb 21, 2012 at 19:33 | comment | added | Jérôme Poineau | Do you have an idea of the answer for the (probably simpler) case of polynomials over $\mathbb{C}$? | |
| Feb 21, 2012 at 17:11 | history | edited | David Feldman | CC BY-SA 3.0 |
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| Feb 21, 2012 at 7:54 | comment | added | Andreas Thom | What has come up in various places is that one associates with a polynomial the probability measure on $\mathbb C$, which is equidistributed on the roots of the polynomial. Now, the space of probability measures has a natural topology and limit points are usually very interesting and special; there are isolated points etc. Equilibrium measures of compact subsets arise this way. | |
| Feb 21, 2012 at 3:36 | history | asked | David Feldman | CC BY-SA 3.0 |