On the sharpness of Jentzsch-Szegö-type theorems (Q1337825)
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scientific article; zbMATH DE number 687083
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the sharpness of Jentzsch-Szegö-type theorems |
scientific article; zbMATH DE number 687083 |
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On the sharpness of Jentzsch-Szegö-type theorems (English)
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13 November 1994
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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.
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