# On the number of real critical points of logarithmic derivatives and the Hawaii conjecture - Mathematics > Classical Analysis and ODEs

Abstract: For a given real entire function $\phi$ with finitely many nonreal zeros, weestablish a connection between the number of real zeros of the functions$Q=\phi-\phi-$ and $Q 1=\phi-\phi-$. This connection leads to a proofof the Hawaii conjecture T.Craven, G.Csordas, and W.Smith, The zeros ofderivatives 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 notexceed the number of nonreal zeros of $\phi$.

Author: Mikhail Tyaglov

Source: https://arxiv.org/