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 Uniqueness of tetration. Small lemma. Kouznetsov Fellow Posts: 151 Threads: 9 Joined: Apr 2008 11/03/2008, 05:10 PM I try to simplify the proof of uniqueness of holomorphic tetration by bo198214. Let $u \in \mathbb{R}$ and $v \in \mathbb{R}$ and $v>0$ Let $\mathcal{S}=\{z\in \mathbb{C} : u<\Re(z) Let $\alpha$ be entire 1-periodic function. Let $\mathcal{D}=\alpha(\mathcal{S})$. According to the Picard’s Little Theorem [1], either $\alpha$ is trivial function (constant), or $\mathcal{D}=\mathbb{C}$ or $\exists c \in \mathbb{C}$ such that $\mathbb{C}=\mathcal{D} \cup c$. Let $\mu(z)=z-\alpha(z) \forall z \in \mathbb{C}$. Let $\mathcal{E}=\mu(\mathcal{S})$ Assume, $\alpha$ is not constant. How to prove that at least one of these two statements is true: $-2\in \mathcal{E}$, $-3\in \mathcal{E}$ ? [1] Weisstein, Eric W. ”Picard’s Little Theorem.” From MathWorld–A Wolfram Web Resource. http://mathworld.wolfram.com/PicardsLittleTheorem.html « Next Oldest | Next Newest »

 Messages In This Thread Uniqueness of tetration. Small lemma. - by Kouznetsov - 11/03/2008, 05:10 PM

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