- #1

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for all z belong to C.

π is pi.

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- Thread starter alvielwj
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- #1

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for all z belong to C.

π is pi.

- #2

HallsofIvy

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How to show "if ...."

for all z belong to C.

π is pi.

but where is your conclusion? What do you want to prove?

- #3

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first show f is bounded,then by the Liouville's theorem, f is constant

- #4

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Suppose that f is an entire function such that f(z) = f(z + 2π ) and f(z) = f(z + 2π i)

for all z belong to C. Use Liouville's theorem to show that f is constant.

Hint: Consider the restriction of f to the square {z = x + iy : 0 <x < 2π ; 0 < y <2π }

- #5

HallsofIvy

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- #6

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I finally know how to use the hint..

At the begining i really dont know how to start..

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