# Student

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 Apr27 comment An entire function $g$ such that $|g(z^2)| \leq e^{|z|}$ and $g(m) = 0 \quad \forall m \in \mathbb{Z}$ is identically $0$Dear Georges, thank you very much for your good wishes. I will indeed take a qualifying exam in the near future so I'm trying to solve exercises from old exams. I figure that since sometimes the professors who teach the basic graduate complex analysis courses use different books, these sort of problems cause more difficulty than originally expected due to one not having the "right" version of a theorem in hand. Apr27 accepted An entire function $g$ such that $|g(z^2)| \leq e^{|z|}$ and $g(m) = 0 \quad \forall m \in \mathbb{Z}$ is identically $0$ Apr27 comment An entire function $g$ such that $|g(z^2)| \leq e^{|z|}$ and $g(m) = 0 \quad \forall m \in \mathbb{Z}$ is identically $0$Thank you very much. I actually thought about this same argument at first, but the book I was looking at had that theorem but with $\sum\frac{1}{|z_k|^{\lambda + 1}} < \infty$ where $\lambda$ is the order of growth so I obviously wasn't able to use it. I see know why some people say it isn't such a great book after all ;) Apr27 revised An entire function $g$ such that $|g(z^2)| \leq e^{|z|}$ and $g(m) = 0 \quad \forall m \in \mathbb{Z}$ is identically $0$edited title Apr27 asked An entire function $g$ such that $|g(z^2)| \leq e^{|z|}$ and $g(m) = 0 \quad \forall m \in \mathbb{Z}$ is identically $0$ Apr27 awarded Citizen Patrol Apr26 awarded Scholar Apr26 accepted Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$ Apr26 comment An application of Runge's theoremBut it has to be a sequence that works for every possible compact set $K \subset A$ so I think that we basically need to do this to get a sequence for each $K_n$ coming from the compact exhaustion, and then that will produce a sequence $f_{n, k}$. Then maybe we can take the diagonal to get a sequence that works for all compacts at once? Apr26 comment An application of Runge's theoremWow that's really helpful. Thank you. Apr26 asked An application of Runge's theorem Sep15 awarded Supporter Sep15 comment Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$Ohh I see. So I was "using" the assumption without even realizing it. Thank you Soarer. Sep15 comment Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$Soarer, I thought about that, but I thought I was making a mistake because I'm not using anything about connectedness in that argument. Sep15 awarded Editor Sep15 revised Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$added 41 characters in body Sep15 comment Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$This is my first question but a friend who recommended the site to me gave me some suggestions on how to ask a question, I hope I did OK. Sep15 awarded Student Sep15 asked Existence of an antiderivative in $U \cup V$ if it exists in both $U$ and $V$