Can we find a holomorphic function $f$ on an annulus $A$ such that $\exp(f(z)) = z$ for all $z$ in $A$, where $A = {z:1/2<|z|<1}$. I guess that we should apply the argument principle or Rouche theorem, but I don't know how to. Could someone give an explicit answer?
$\begingroup$
$\endgroup$
1
-
2$\begingroup$ See math.stackexchange.com/q/2151918/42969 $\endgroup$– Martin RApr 23 at 17:57
Add a comment
|