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 Questions about Kneser... JmsNxn Long Time Fellow Posts: 517 Threads: 90 Joined: Dec 2010 02/16/2021, 12:46 AM (This post was last modified: 02/16/2021, 06:52 AM by JmsNxn.) Interesting, so we'd have branches of $\text{slog}$ that are holomorphic in a neighborhood of $L$ then. Unlike with the logarithm where no branch is holomorphic in a neighborhood of $0$. I think the trouble with this construction will be getting $\Phi$ to be well behaved as we grow $\Re(s)$. And not to mention, getting general growth lemmas on the various branches of $\text{slog}$. The only work around I see would be to take the inverse iteration, $ \text{pent} = \text{tet}_{\text{Kneser}}^{\circ n} \Phi(s-n)\\$ Where of course, we'd have to modify $\Phi$ to converge in this circumstance. And here we'd probably lose any chance of it being real-valued. I'm going to keep this on a backburner and come back to it later. I'm going to stay focused on $\mathcal{C}^\infty$ proofs for the moment. « Next Oldest | Next Newest »

 Messages In This Thread Questions about Kneser... - by JmsNxn - 02/14/2021, 04:28 AM RE: Questions about Kneser... - by sheldonison - 02/14/2021, 05:00 PM RE: Questions about Kneser... - by JmsNxn - 02/16/2021, 12:46 AM

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