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Jul 25, 2012 at 12:27 vote accept Joël
Jul 25, 2012 at 12:26 comment added Joël Thanks. I will in a few days, when I have thought at the best way to formulate it.
Jul 25, 2012 at 8:22 comment added Andreas Thom I think your new (or initial) question is really interesting. Why don't you ask this as a separate question?
Jul 25, 2012 at 0:10 comment added Joël Thanks. I didn't see this analytic condition coming ! Because of it, it seems indeed very hard to characterize the image. Here I must confess that the initial problem I met in my research was different: a version mod $p$ (and actually for $p=2$) of the same question. That is, what polynomial in $\mathbb{F}_p[x,y,z]$ is the reduction of a Fricke polynomial. And here, computations seems to show that the image is pretty big.
Jul 24, 2012 at 19:31 history answered Andreas Thom CC BY-SA 3.0