Questions about Kneser...

[sheldonison]

So I've been running through my head a question. But in order to resolve that question, I need to better understand Kneser's construction. The premise of this post is to talk about constructing pentation from Kneser's construction.

Now, I know that,

\( \text{tet}_{\text{Kneser}}(s):\mathcal{H}\to\mathbb{C} \)

Where \( \mathcal{H} = \{\Im(s) > 0\} \). And I know it tends to a fixed point \( L \) as \( \Re(s) \to -\infty \). (Or is it multiple fixed points?)
...This depends on Kneser though, does it ever attain the value \( L \) other than at \( -\infty \)?
...
I really wish there was more supplemental literature on Kneser's construction other than what's available on this forum... -_-

Hey James,
The two fixed points are L, L* in the upper/lower halves of the complex plane.  Kneser tends to L as \( \Im(z)\to\infty;\;\;\Re(z)\to-\infty \)
Wherever \( \text{tet}(z)=L+2n\pi i;\;\;\text{tet}(z+1)=L \) and this happens an infinite number of times in the complex plane
See this mathstack post for a good readable overview of Kneser.