Generalizes Lavrentiev's and Mergelyan's theorems to uniform polynomial approximation that avoids any prescribed countable set of values on suitable compact sets in the complex plane.
Lavrent′ev’s approximation theorem with nonvanishing polyno- mials and universality of zeta-functions
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Polynomial approximation avoiding values in countable sets
Generalizes Lavrentiev's and Mergelyan's theorems to uniform polynomial approximation that avoids any prescribed countable set of values on suitable compact sets in the complex plane.