On the distribution of zeros of entire functions

Author:
A. R. Reddy

Journal:
Proc. Amer. Math. Soc. **45** (1974), 105-112

MSC:
Primary 30A66

DOI:
https://doi.org/10.1090/S0002-9939-1974-0369697-3

MathSciNet review:
0369697

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Abstract | References | Similar Articles | Additional Information

Abstract: Let be any transcendental entire function. Let denote the absolute value of the zero of which is nearest to the origin. Ålander, Erdös and Rényi, and Pólya have investigated the relation between and the growth of the function . Let denote the largest disk about the origin where is univalent. Boas, Levinson, and Pólya have obtained some relations between the growth of the function and . Recently Shah and Trimble have sharpened the results of Boas and Pólya. 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 with the growth of .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1974-0369697-3

Keywords:
Zeros of entire functions,
zero-free disks,
univalent disks

Article copyright:
© Copyright 1974
American Mathematical Society