|Nov26-07, 12:25 PM||#1|
Suppose f is an entire function such that [latex]f(z) = f(z+2\pi)[/latex]
and [latex]f(z)=f(z+2\pi i)[/latex] for all z [latex]\epsilon[/latex] 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 :)
|Nov26-07, 09:17 PM||#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?
|Nov26-07, 09:37 PM||#3|
not just completely determined, but actually that it maps that square onto its range of values.
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