Johan Andersson, SU: Mergelyan's theorem with zero-free polynomials

Abstract: We consider the question of whether a continuous function that is analytic and zero-free in the interior of a compact set K with connected complement can be approximated by a polynomial  that is zero-free on K. Whe show that this is true in some special cases and relates the general question with a related question on Voronin universality for the Riemann zeta function.