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Liouville's theorem (Complex A)

  1. Apr 15, 2015 #1
    Assume |f(z)| >= 1/3|e^(z^2)| for all z in C and that f(0) = 1 and that f(z) is entire. Prove that f(z) = e^(z^2) for all z in C.

    How do you start for this.
  2. jcsd
  3. Apr 15, 2015 #2


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    Let g(z) = e^(z^2) and consider the function g(z)/f(z). Show that it is entire and has a bounded modulous. You should be able to continue from there.
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