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Computational Methods and Function Theory 6 (2006), No. 1, 243--252
Copyright Heldermann Verlag 2006

Solution of a Problem of Edwards and Hellerstein

James Langley
jkl@maths.nott.ac.uk , School of Mathematical Sciences, University of Nottingham, NG7 2RD, United Kingdom.

[Abstract-pdf] [Abstract-ps]

Let f be a real transcendental entire function of finite order with finitely many non-real zeros and let F be the Newton function of f. Then the set { z ∈ C : Im z > 0, Im F(z) < 0 } has no unbounded components.

Keywords: Entire function, real zeros, Newton function.

MSC 2000: 30D20, 30D35.

[FullText-pdf (258 K)] [FullText-ps (431 K)]