08/27/2009, 06:52 PM

(08/27/2009, 06:21 PM)jaydfox Wrote: [quote='bo198214' pid='3861' dateline='1251390997']Well it took quite some while until I got what he is talking about. Though I hoped my description would make it easier, perhaps however its just a write-up for my own understanding. But the base idea is really: we have already some cool super-logarithm (the rslog) which however is not real on the real line. So we make it real on the real on the real line with help of the Riemann mapping theorem (which he does not mentioned once in his article, he just assumed that everyone of course knows what he means!).

I apparently don't understand them well enough to string the steps together mentally and have one of those "Ah-ha!" moments.

The real kslog should map the upper half plane H again to H. Thatswhy we put .

Quote:I'm assuming it maintains the approximation of the regular slog near the fixed point?Unfortunately I dont know. I have to better understand how this approximation looks. Perhaps I can then derive that it is true for Kneser's slog as well.

Quote:You mentioned somewhere having a means to compute values for Kneser's slog: perhaps we should see how well they match up with the islog?No. The Riemann mapping theorem is hard computationally, i.e. for two given regions (how are they given?) to compute the conformal map between them. I gave it once a vague try (indeed there is also a constructive/approximative way to compute those conformal maps, also given in "Henrici", but I think they are way beyond any current computer performance for our problem yet)

However Kneser also suggests a certain series expansion (with fractional exponents) at the fixed point. But I didnt find a way to compute the coefficients yet.

Quote:And you mention the uniquess criterion that you outlined in that paper: are you saying then that you don't consider this criterion proven?I gave a proof, verify yourself! But honestly there are so many cases where I found errors in my derivations that I want to wait for the reviewers opinions, before I believe it myself. Though I have a good feeling about it