Zeros of optimal polynomial approximants: Jacobi matrices and   Jentzsch-type theorems
  We study the structure of the zeros of optimal polynomial approximants to reciprocals of functions in Hilbert spaces of analytic functions in the unit disk. In many instances, we find the minimum possible modulus of occurring zeros via a nonlinear extremal problem associated with norms of Jacobi matrices. We examine global properties of these zeros and prove Jentzsch-type theorems describing where they accumulate. As a consequence, we obtain detailed information regarding zeros of reproducing kernels in weighted spaces of analytic functions. 
Catherine B\'en\'eteau, Dmitry Khavinson, Constanze Liaw, Daniel Seco,   and Brian Simanek
math.CA math.CV