Geodesic
A Note on Divisibility in H∞(X)
Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 458-469

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Let X be a Riemann surface, and H ∞(X) the ring of bounded holomorphic functions in X. We offer here a question on divisibility in H∞ (X), and then give in Section 2 a condition in which the answer is yes (Corollary 2 to Lemma 1). In Section 3 we use part 2 to prove a theorem on the separation of points by H ∞(X). In Section 4 we study X/H∞ (X).If f is meromorphic in X and z ∈ X, then by o(f, z) we mean the order of f at z. (We agree that o(f, z) = ∞ if f ≡ 0.) Let h be memomorphic in X; then h might be said to be of bounded type if h = f/g where f,g ∈ H∞(X), g ≠ 0. 
Forelli, Frank. A Note on Divisibility in H∞(X). Canadian journal of mathematics, Tome 36 (1984) no. 3, pp. 458-469. doi: 10.4153/CJM-1984-028-7
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