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Complex analysis question

  1. Apr 23, 2009 #1
    1. The problem statement, all variables and given/known data
    if an entire function satisfies f(z+i)=f(z) and f(z+1)=f(z), must the function be constant?


    2. Relevant equations



    3. 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.
     
  2. jcsd
  3. Apr 23, 2009 #2
    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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