• Corpus ID: 119555204

Zero-free polynomial approximation on a chain of Jordan domains

@article{Gauthier2012ZerofreePA,
  title={Zero-free polynomial approximation on a chain of Jordan domains},
  author={Paul M. Gauthier and Greg E. Knese},
  journal={arXiv: Complex Variables},
  year={2012}
}
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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