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Holomorphic function

  1. Sep 27, 2011 #1
    1. The problem statement, all variables and given/known data
    If f: D(0,1) -> C is a function (C = set of complex numbers), and both f^2 and f^3 are holomorphic, then prove that f is holomorphic.


    2. Relevant equations



    3. The attempt at a solution
    Setting f = (f^3) / (f^2), then I think we need to look at the zeros of the function? Not sure where to go from there.
     
  2. jcsd
  3. Sep 27, 2011 #2

    micromass

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    Split up in two cases:

    1) The set of zeroes of [itex]f^2[/itex] doesn't have an accumulation point (= the zeroes are isolated)

    2) [itex]f=0[/itex].
     
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