Distance between a Maximum Modulus Point and Zero Set of an Entire Function

Authors: Ostrovskii I.; Ersin Üreyen A.

Source: Complex Variables, Volume 48, Number 7, July 2003 , pp. 583-598(16)

Publisher: Taylor and Francis Ltd

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Abstract:

Let f be an entire function of finite positive order. A maximum modulus point is a point w such that |f(w)|= max {|f(z)|:|z=|w|}. We obtain lower bounds for the distance between a maximum modulus point w and the zero set of f. These bounds are valid for all sufficiently large values of |w|.

Keywords: Entire function; Order; Proximate order; Strong proximate order; Type; 2000 AMS Subject Classification: 30D20

Document Type: Research article

DOI: 10.1080/0278107031000120431

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