Timeline for When are entire functions surjective?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| May 27, 2017 at 7:42 | comment | added | Alexandre Eremenko | See mathoverflow.net/questions/270804/surjective-entire-functions/… | |
| Jun 4, 2010 at 14:39 | comment | added | Malik Younsi | @Saul : We can conclude that $f$ IS surjective. | |
| Jun 3, 2010 at 20:59 | comment | added | Saul Glasman | But certainly if there is no $\alpha \in \mathbb{C}$ such that $\frac{f'(z)}{f(z) - \alpha}$ is entire, we can conclude that $f$ is not surjective. | |
| Jun 3, 2010 at 12:51 | comment | added | babubba | @Pete L. Clark: Hence the 'maybe' in the post. I was thinking about a useful/practical criterion but nothing came to mind. | |
| Jun 3, 2010 at 12:36 | comment | added | Pete L. Clark | I don't see how Picard's theorem, or Roland Bacher's remark, is useful in practice to determine whether an entire function is surjective. | |
| Jun 3, 2010 at 10:24 | comment | added | dke | +1. And to show this, it's probably worth looking at en.wikipedia.org/wiki/Weierstrass_factorization_theorem | |
| Jun 3, 2010 at 10:13 | comment | added | Roland Bacher | Indeed. And it is surjective if and only if it not of the form $e^{h(z)}+\alpha$ for a suitable constant $\alpha$ and a suitable entire function $h(z)$. | |
| Jun 3, 2010 at 9:45 | history | answered | babubba | CC BY-SA 2.5 |