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Entire function

  1. Mar 29, 2012 #1
    Difficult with this problem.
    Find all entire functions f such that |f(z)| = 1 for all z with |z| = 1.

    Are there any vigorous proofs?
  2. jcsd
  3. Mar 30, 2012 #2

    By the minimum modulus theorem, such a function must be constant...

  4. Mar 30, 2012 #3
    So the function f(z)=z is a constant then??
  5. Mar 30, 2012 #4

    Oops! I missed the "for all |z| = 1" in the OP...

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