Approximation by polynomials and Blaschke products having all zeros on a circle

@article{Farmer2010ApproximationBP,
  title={Approximation by polynomials and Blaschke products having all zeros on a circle},
  author={David W. Farmer and Pamela Gorkin},
  journal={arXiv: Complex Variables},
  year={2010}
}
We show that a nonvanishing analytic function on a domain in the unit disc can be approximated by (a scalar multiple of) a Blaschke product whose zeros lie on a prescribed circle enclosing the domain. We also give a new proof of the analogous classical result for polynomials. A connection is made to universality results for the Riemann zeta function. 
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