Computational Methods and Function Theory 4 (2004), No. 2, 341--354
Copyright Heldermann Verlag 2004
Adem E. Üreyen
ureyen@fen.bilkent.edu.tr , Department of Mathematics, Bilkent University, 06800 Bilkent, Ankara, Turkey.
A maximum modulus point of an entire function f is a point w such that |f(w)| = max{|f(z)|:|z|=|w|}. Denote by R(w,f) the distance between a maximum modulus point w and the zero set of f. In 1938, A. J. Macintyre obtained lower asymptotic estimates for R(w,f) as |w| approaches infinity valid outside of an exceptional set. The problem of asymptotic estimates valid for all sufficiently large |w| was studied by I. V. Ostrovskii and the author for functions of finite positive order. In this paper, we study this problem for functions of either zero or infinite order.
Keywords: Entire function, zero order, infinite order, proximate order, type.
MSC 2000: 30D20.
[FullText-pdf (328 K)] [FullText-ps (268 K)]