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Liouville's Theorem

  1. Nov 26, 2007 #1
    Suppose f is an entire function such that [itex]f(z) = f(z+2\pi)[/itex]
    and [itex]f(z)=f(z+2\pi i)[/itex] for all z [itex]\epsilon[/itex] C. How can you use Liouville's theorem to show f is constant..

    any help on that please to get me started off.. thnx a lot :)
  2. jcsd
  3. Nov 26, 2007 #2
    The two given relations tell you that [tex]f[/tex] is completely determined by its values in a square of side length [tex]2\pi[/tex]... what do you need to show about [tex]f[/tex] to use Liouville? Can you get it from this info now?
  4. Nov 26, 2007 #3


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    not just completely determined, but actually that it maps that square onto its range of values.
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