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On a compact subset of the plane with connected complement, is it possible touniformly approximate a continuous function, holomorphic and non-vanishing onthe interior, with polynomials non-vanishing on the entire compact set? In thisbrief note, we recall the surprising connection between this question and theRiemann hypothesis and proceed to provide an affirmative answer for a "chain"of Jordan domains.

Zero-free polynomial approximation on a chain of Jordan domains