On Localization of Zeros of an Entire Function of Finite Order of Growth

On Localization of Zeros of an Entire Function of Finite Order of Growth

The aim of the article is to find conditions on coefficients of a Taylor expansion of an entire function of finite order of growth in C that guarantee a specified number of zeros. If the Taylor coefficients of f are real we also give conditions to determine whether the number of real and imaginary z...

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Veröffentlicht in:Complex analysis and operator theory 2017-02, Vol.11 (2), p.393-416
Hauptverfasser: Kytmanov, Alexander M., Khodos, Olga V.
Format: Artikel
Sprache:eng
Schlagworte:
Analysis
Entire functions
Mathematics
Mathematics and Statistics
Operator Theory
Thermal expansion
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Beschreibung
Zusammenfassung:The aim of the article is to find conditions on coefficients of a Taylor expansion of an entire function of finite order of growth in C that guarantee a specified number of zeros. If the Taylor coefficients of f are real we also give conditions to determine whether the number of real and imaginary zeros is finite or infinite, and whether they are real or imaginary.
ISSN:1661-8254
1661-8262
DOI:10.1007/s11785-016-0606-8