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How to show that an entire function is a constant function using Liouville's Theorem

we have:
f is entire such that f(z) = f(z + 2Pi) and f(z) = f(z+2*i*Pi) for all z in the complex plane.
need to show that f is constant.

By Liouville's them, we only need to show f is bounded.

there's a hint which says to restrict f to the square S = {z=x+iy: 0=<x=<2Pi, 0=<y=<2pi}

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my working so far:

to show f is bounded maybe look at x=0, y=0, x=2Pi, y=2Pi? i'm not sure what this would yield though
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anzerftum
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yyug
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around
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what do you know about continuous functions on a compact set.
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Original post by around
what do you know about continuous functions on a compact set.


they're bounded? thats it? then liouville's follows?
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Original post by anzerftum
they're bounded? thats it? then liouville's follows?


Pretty much.

This is why all elliptic functions are meromorphic (the question is not utterly pointless).

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