Timeline for How to prove that $e^{zw}$ can not be written as a rational expression in functions in $z$ and in $w$?
Current License: CC BY-SA 3.0
15 events
| when toggle format | what | by | license | comment | |
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| May 18, 2016 at 6:42 | history | edited | GH from MO |
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| Apr 18, 2011 at 18:46 | vote | accept | zamanjan | ||
| Apr 18, 2011 at 2:11 | comment | added | GH from MO | @Gerald: This problem is purely algebraic. Many formal power series don't converge at all (off the center) yet they participate in the problem. | |
| Apr 18, 2011 at 2:00 | answer | added | GH from MO | timeline score: 15 | |
| Apr 18, 2011 at 1:56 | comment | added | Gerald Edgar | $$e^{zw} = \exp(\exp(\log z + \log w))$$ I left out the "rational" part of the question. And consideration of domains... | |
| Apr 18, 2011 at 1:10 | comment | added | KConrad | Michael: you want to show $e^{z^2}$ is not a rational function of $z$. Or instead let $w = 2$ instead of $w = z$. | |
| Apr 17, 2011 at 23:56 | answer | added | user12806 | timeline score: 4 | |
| Apr 17, 2011 at 20:10 | comment | added | Martin Brandenburg | 1+, very interesting question. I've also worked on that to find explicit examples that the functor from complex manifolds to complex locally ringed spaces does not preserve products. | |
| Apr 17, 2011 at 19:51 | comment | added | zamanjan | Thanks Fedor, indeed my original title was not good. | |
| Apr 17, 2011 at 19:33 | comment | added | Fedor Petrov | @Gerald: I've tried to make the title more related to the question | |
| Apr 17, 2011 at 19:32 | history | edited | Fedor Petrov | CC BY-SA 3.0 |
title changed
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| Apr 17, 2011 at 19:24 | comment | added | Gerald Edgar | Presumably the vote to close is because the question in the title is easy as Michael showed. (Homework level for a first course in complex variables.) So the title should be changed! | |
| Apr 17, 2011 at 19:03 | comment | added | user12806 | Zamanjan search to prove that $e^{zw} \neq Q(f_1(z),...,f_k(z),g_1(w),...,g_n(w))$ for all rational function $Q$ and all series $f_1(z),...,f_k(z),g_1(w),...,g_n(w)$. | |
| Apr 17, 2011 at 18:53 | comment | added | Michael Lugo | For the particular case you're interested in, wouldn't it suffice to let $z = w$ and show that $e^{2z}$ can't be written as a rational function of $z$? | |
| Apr 17, 2011 at 17:29 | history | asked | zamanjan | CC BY-SA 3.0 |