Difference between revisions of "Talk:Aufgaben:Problem 14"

Revision as of 15:32, 31 December 2014

What should this "Pierre's lemma" be? It's clearly false: let \( f = u + iv \) (with \( u \) and \( v \) real-valued) be any non-constant analytic function; then clearly \( u \) or \( v \) is not constant. Following "Pierre's lemma" they should both be analytic, but we've showed in Ch. II.3 that any analytic real-valued function is constant, which is a contradiction. (And in any case, in the "proof" \( a \) and \( b \) should be different from \( 0 \)...)

Cheers, the tables

Let's say u and v are meromorphic and everything is okay again, I guess. f has a Taylorexpansion, can be divided into an a and ib part, yadiyadiya, v is elliptic and so on.

Cheers, the guy hating you for pointing out his mistakes

I'm sorry, but I guess somebody has to point out mistakes when there are any, even if it's a tough job... Anyway, I fear it still doesn't work: if they're meromorphic, then they're holomorphic at "almost every point", which for the previous argument means that they're constant almost everywhere, which of course is not the case for all holomorphic functions f. I didn't want to waste your work, but we can't write it in the MMP proof like that, don't you agree?

I was just joking. Due to my strange academic sense of humor, people usually think I can't handle criticism but I actually love it. That's why I like cooking with my girlfriend so much.

Now back to the serious stuff: It's a sketch so far I did for the people solving the problem. They'll work on it, don't worry. If f has a Taylorexpansion, then u and v do from the argument already there, so v has no poles. Then use part a). That should make you happy, I guess.

Otherwise please correct me again. Happy new year by the way. A.