Help me please.

Let be an entire function :

.

Prove that is constant. (Don't use Picard Theorem).

Thanks!

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- Dec 16th 2011, 02:04 PMsinichkoComplex analysis
Help me please.

Let be an entire function :

.

Prove that is constant. (Don't use Picard Theorem).

Thanks! - Dec 16th 2011, 03:06 PMxxp9Re: Complex analysis
Hint: find a mobius map g that maps the real line to the unit circle C, then the domain of g(f), D={g(f(z))} has no intersection with C. Since D is connected, D is either inside C or outside C, then {1/g(f(z))} is inside C. Anyway this contradicts the maximal module principle.