Timeline for Meromorphic function on $\mathbb{C}$ algebraic over $\mathbb{C}(z)$
Current License: CC BY-SA 4.0
7 events
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| Nov 19, 2021 at 19:18 | history | edited | GH from MO | CC BY-SA 4.0 |
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| Nov 19, 2021 at 19:14 | comment | added | GH from MO | Nice. Your proof is similar to the argument in my post, but of course subtly different. I should add that for Casorati-Sochotski-Weierstrass you probably need that $f(1/z)$ has an isolated singularity at $z=0$. This is clear of course, since $f$ has at most $d$ poles (applying your argument for $a=0$ and for $1/f$ in place of $f$). | |
| Nov 19, 2021 at 19:14 | comment | added | Wojowu | Lovely, thank you for elaborating! | |
| Nov 19, 2021 at 18:39 | history | edited | Alexandre Eremenko | CC BY-SA 4.0 |
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| Nov 19, 2021 at 18:32 | comment | added | Alexandre Eremenko | Sure. With a few extra words you can appeal to Casoratti-Weierstrass theorem. | |
| Nov 19, 2021 at 14:50 | comment | added | Wojowu | Is there a way to justify your last "therefore $f$ is rational" without appealing to something like great Picard theorem? | |
| Nov 19, 2021 at 14:17 | history | answered | Alexandre Eremenko | CC BY-SA 4.0 |