Zero-free polynomial approximation on a chain of Jordan domains

P. M. Gauthier; Greg Knese

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arXiv · 1208.6549

Zero-free polynomial approximation on a chain of Jordan domains

P. M. Gauthier·Greg Knese

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Abstract

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

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P. M. Gauthier, Greg Knese. 2012-08-31. Zero-free polynomial approximation on a chain of Jordan domains. https://arxiv.org/abs/1208.6549

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