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References (7)
-
A. Macintyre (1938)
WIMAN'S METHOD AND THE ‘FLAT REGIONS’ OF INTEGRAL FUNCTIONSQuarterly Journal of Mathematics
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J. Earl, W. Hayman (1991)
Smooth majorants for functions of arbitrarily rapid growthMathematical Proceedings of the Cambridge Philosophical Society, 109
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Sh Strelitz (1972)
Asymptotic properties of analytical solutions of differential equations (in Russian) -
I. Ostrovskii, A. Üreyen (2003)
Distance between a Maximum Modulus Point and Zero Set of an Entire FunctionComplex Variables, Theory and Application: An International Journal, 48
-
B. Levin (1964)
Distribution of zeros of entire functions -
A. Horadam (1958)
PROJECTION OF AN INVARIANT LOCUS IN [8] FROM A SOLID LYING ON ITQuarterly Journal of Mathematics, 9
-
J P Earl, W K Hayman (1991)
Smooth majorants for functions of arbitrarily rapid growth, MathProc. Camb. Phil. Soc, 109
- Publisher
- Springer Journals
- Copyright
- Copyright © 2004 by Heldermann Verlag
- Subject
- Mathematics; Analysis; Computational Mathematics and Numerical Analysis; Functions of a Complex Variable
- ISSN
- 1617-9447
- eISSN
- 2195-3724
- DOI
- 10.1007/BF03321074
- Publisher site
- See Article on Publisher Site
Abstract
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¦ →∞ 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.
Journal
Computational Methods and Function Theory – Springer Journals
Published: Mar 7, 2013