On the sharpness of Jentzsch-Szegö-type theorems. (English) Zbl 0805.30002
It is proved in this paper that there exist power series with radius of convergence 1, such that their partial sums have (as far as it is consistent with the Theorems of Jentzsch and Szegö): – a prescribed number of zeros in \(| z | \leq R\), – a prescribed set of limit- points of zeros. It is also proved that there exists a universal power series with a “universal distribution” of the zeros of its partial sums.
Reviewer: W.Gehlen (Trier)
MSC:
| 30B10 | Power series (including lacunary series) in one complex variable |
| 30C15 | Zeros of polynomials, rational functions, and other analytic functions of one complex variable (e.g., zeros of functions with bounded Dirichlet integral) |
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