Approximation by translates of Taylor polynomials of the Riemann zeta function (Q934521)
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scientific article; zbMATH DE number 5305516
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Approximation by translates of Taylor polynomials of the Riemann zeta function |
scientific article; zbMATH DE number 5305516 |
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Approximation by translates of Taylor polynomials of the Riemann zeta function (English)
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29 July 2008
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From the authors' summary: ``We show that each function holomorphic on a compact set with connected complement can be approximated by translates of Taylor polynomials of the Riemann zeta function. From this it can be concluded that each entire function can be approximated by translates of Taylor polynomials of the \(\zeta\)-function.'' For the proof the author uses a result of \textit{V. Nestoridis} in [Ann. Inst. Fourier 46, No. 4, 1293--1306 (1996; Zbl 0865.30001)]. The paper ends with the remark that the universality property proved for the Riemann zeta function is shared by almost all entire functions. But one knows explicitly not one other entire function aside the Riemann zeta function (and its close cousins, e.g., other zeta functions) having such a universality property.
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Voronin's theorem
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