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

摘要

We show that a nonvanishing analytic function on a domain in the unit disccan be approximated by (a scalar multiple of) a Blaschke product whose zeroslie on a prescribed circle enclosing the domain. We also give a new proof ofthe analogous classical result for polynomials. A connection is made touniversality results for the Riemann zeta function.