[2014] The secondary fixpoint issue.

[tommy1729]

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Seems unlikely that sexp contains none of these n-ary fixpoints ?!

And as for the functional equation f(x+1) = exp(f(x)) + 2pi i that is on another branch. So that does not seem to help.

Conjecture: if \( \text{sexp}(z)=L \), than for some positive integer n, there is a non-zero integer m such that \( \text{sexp}(z-n)=L+2m\pi i \)

This would apply for L equals any fixed point of exp(z). This conjecture would apply to both the Kneser solution, and the secondary fixed point solution. I think it can be proven by showing for these two solutions, that sexp(z-n)<>L as n goes to infinity.

Wait a minute , we have sexp(R + oo i) = L or conj(L) for all real R and all real oo !?

I thought we all agreed on that for years ?

But R + oo i - n is also of the form R + oo i.

??
Now Im even more confused.

Thanks for the reply though.

regards

tommy1729