Zero-free polynomial approximation on a chain of Jordan domains

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.

7 pages, minor corrections to intro. To appear in Annales des sciences mathématiques du Québec

References in corpus (1)

• Mergelyan's approximation theorem with nonvanishing polynomials and universality of zeta-functions

Cited by in corpus (2)

• On the zero-free polynomial approximation problem
• Polynomial approximation avoiding values in countable sets