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arXiv · 0902.0413

On the number of real critical points of logarithmic derivatives and the Hawaii conjecture

Mikhail Tyaglov
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Abstract

For a given real entire function $\phi$ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions $Q=(\phi'/\phi)'$ and $Q_1=(\phi''/\phi')'$. 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 P\'olya-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 $\phi$.

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Mikhail Tyaglov. 2009-02-03. On the number of real critical points of logarithmic derivatives and the Hawaii conjecture. https://doi.org/10.1007/s11854-011-0011-1

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