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Homework Help: Complex analysis zero/branch problem

  1. Apr 2, 2008 #1
    1. The problem statement, all variables and given/known data

    Let f be a holomorphic function in the open subset G or C. Let the point Z of G be a zero of f of order m. Prove that there is a branch of f^(1/m) in some open disk centered at Z

    2. Relevant equations

    Branch- a continuous function g in G such that, for each x in G, the value of g(x) is a value of f^(1/m)

    3. The attempt at a solution

    My biggest problem is formulating a proof that a branch exists. If somebody could give me a push start on how to start and formulate the proof that the branch exists I will be able to figure out the rest.
  2. jcsd
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