On the location of the zeros of analytic functions (Q916817)

The authors derive lower bounds for the moduli of the zeros of functions f analytic in a disc \(| z| \leq t\) whose Taylor coefficients \(a_ j\) satisfy certain constraints. The first theorem applies to constraints \(| \arg a_ j| \leq \alpha \leq \pi /2\) and monotonicity conditions \[ | a_ 0| \leq t| a_ 1| \leq...\leq t^ k| a_ k| \geq t^{k+1}| a_{k+1}| \geq..., \] for some integer k, and the second theorem to conditions \[ 0<Re a_ 0\leq t Re a_ 1\leq...\leq t^ k Re a_ k\geq t^{k+1} Re a_{k+1}\geq.... \] These bounds are similar to but sharper than those given by \textit{A. Aziz} and \textit{Q. G. Mohammad}, J. Math. Anal. Appl. 75, 495-502 (1980; Zbl 0444.30006).