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

For a given real entire function $\varphi$ with finitely many nonreal zeros, we establish a connection between the number of real zeros of the functions $Q=({\varphi }^{\mathrm{\prime }}\mathrm{/}\varphi {)}^{\mathrm{\prime }}$ and $Q_1=({\varphi }^{\mathrm{\prime }\mathrm{\prime }}\mathrm{/}{\varphi }^{\mathrm{\prime }}{)}^{\mathrm{\prime }}$. 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 $\varphi$.