Liouville's Theorem

1. Nov 26, 2007

smoothman

Suppose f is an entire function such that $f(z) = f(z+2\pi)$
and $f(z)=f(z+2\pi i)$ for all z $\epsilon$ 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. Nov 26, 2007

Xevarion

The two given relations tell you that $$f$$ is completely determined by its values in a square of side length $$2\pi$$... what do you need to show about $$f$$ to use Liouville? Can you get it from this info now?

3. Nov 26, 2007

mathwonk

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