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Complex analysis question

  • Thread starter playa007
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  • #1
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Homework Statement


if an entire function satisfies f(z+i)=f(z) and f(z+1)=f(z), must the function be constant?


Homework Equations





The Attempt at a Solution


It's true that f(0) = f(k) = f(ik) where k is an integer. I'm wondering whether I can apply Liouville's theorem into this somehow or if it's not constant at all on how to construct a counterexample.
 

Answers and Replies

  • #2
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Hmm...well I think you can show that all of the function values are determined by the function values on a certain compact set. Since the continuous image of a compact set is bounded, the function must be bounded and so you can apply Liouville's theorem.
 

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