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Complex analysis, holomorphic functions, automorphic group actions and forms, pseudoconvexity, complex geometry, analytic spaces, analytic sheaves.

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Relation between partially computable function and complex function

Any complex-valued function on $\mathbb{N}$ can be extended to an entire function, so the answer is "yes." This follows from Theorem 15.13 of Rudin's Real and Complex Analysis, which states that for a …
Keenan Kidwell's user avatar