On the Distribution of Zeros of Entire Functions
نویسنده
چکیده
Let f(z) be any transcendental entire function. Let r, denote the absolute value of the zero z. of f '(z) which is nearest to the origin. Alander, Erdö's and Renyi, and Polya have investigated the relation between r, and the growth of the function /(z). Let s, denote the ... fz largest disk about the origin where / (z) is univalent. Boas, Levinson, and Polya have obtained some relations between the growth of the function f(z) and s ,. Recently Shah and Trimble have sharpened the results of Boas and Polya. We present here results in a different direction, generalizing the above quoted results. We also present results connecting the zero-free disks and the univalent disks about the origin of the normalized remainders of f(z) with the growth of /(z).
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