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Homework Help: Number of zero's of holomorphic function

  1. Jun 8, 2013 #1
    1. The problem statement, all variables and given/known data

    Let f(z) be holomorphic in the open unit disc taking real values only on the real axis.show that f has at most one zero in the open disc.

    2. Relevant equations

    Rouche's theorem,the argument principle.

    3. The attempt at a solution
    obviously,f does not have non-real zero's .I need help in counting the zero's by using the argument principle.
    Last edited: Jun 8, 2013
  2. jcsd
  3. Jun 8, 2013 #2


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    I'm not an expert, but is argument is zero at +1 and -1 and can't be zero anyplace else as the contour winds around the boundary of the unit circle. What are the possibilities for the winding number?
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