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Complex analysis/entire function question

  1. Sep 21, 2011 #1
    1. The problem statement, all variables and given/known data

    Suppose f is an entire function, satisfying

    f(z + a) = f(z) = f(z + b), for all z [itex]\in[/itex] C; where a; b are nonzero, distinct complex numbers.

    Prove that f is constant.

    2. Relevant equations

    Loville's theorem: if f is bounded & entire, then f is constant.

    3. The attempt at a solution

    where would I begin to prove this function is bounded? any hint would be appreciated!
  2. jcsd
  3. Sep 21, 2011 #2
    Yes, show that the function is bounded. This isn't particularly hard to do because it is periodic!
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