 Solution

ID: past-exam-of-the-algebra-and-analysis-ii-for-mathematics-and-philosophy-course-of-the-university-of-oxford/2013/6/c/solution

f holomorphic on C, z \in C sup ∣ f (z) ∣ < \infty ⟹ f constant .

For example, the Cauchy derivative estimate on a circle of radius

R

gives

∣ f^{'} (z) ∣ \leq M / R

. Letting

R \to \infty

gives

f^{'} = 0

everywhere, proving the conclusion.

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