Abstract
Given a compact set E in \(\mathbb{C}\) and a function f holomorphic on E, we investigate the distribution of zeros of rational uniform approximants \(\{{r}_{n,{m}_{n}}\}\) with numerator degree≤n and denominator degree≤m n , where \({m}_{n} = o(n/\log n)\) as n→∞. We obtain a Jentzsch–Szegő type result, i.e., the zero distribution converges weakly to the equilibrium distribution of the maximal Green domain Eρ(f) of meromorphy of f if f has a singularity of multivalued character on the boundary ∂Eρ(f). Further, we show that any singular point of f on the boundary ∂Eρ(f), that is not a pole, is a limit point of zeros of the sequence \(\{{r}_{n,{m}_{n}}\}\).
Published Version
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