Uloženo v:
| Hlavní autor: | |
|---|---|
| Médium: | Preprint |
| Vydáno: |
2009
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| Témata: | |
| On-line přístup: | https://arxiv.org/abs/0902.0413 |
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Obsah:
- For a given real entire function $ϕ$ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions $Q=(ϕ'/ϕ)'$ and $Q_1=(ϕ''/ϕ')'$. This connection leads to a proof of the Hawaii conjecture [T.Craven, G.Csordas, and W.Smith, The zeros of derivatives of entire functions and the Pólya-Wiman conjecture, Ann. of Math. (2) 125 (1987), 405--431] stating that the number of real zeros of $Q$ does not exceed the number of nonreal zeros of $ϕ$.