On the zeros of the second derivative of real entire functions (Q2367335)

Let \(f\) be an entire function of infinite order. Suppose that \(f\) is real on the real axis and all its zeros are real. \textit{T. Sheil-Small} conjectured, in connection with his solution of the known Wiman problem [Ann. Math., II. Ser. 129, No. 1, 179-193 (1989; Zbl 0671.30027)] that \(f''\) must have infinitely many zeros. The paper contains the proof of the validity of the conjecture in case the number of zeros of \(f\) is finite.