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CERCLES DE REMPLISSAGE FOR ENTIRE FUNCTIONS

Published online by Cambridge University Press:  01 January 1999

P. C. FENTON  and
JOHN ROSSI
P. C. FENTON
Affiliation:
Department of Mathematics, University of Otago, Dunedin, New Zealand
JOHN ROSSI
Affiliation:
Department of Mathematics, Virginia Tech, Blacksburg, VA 24060, USA
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Abstract

It is shown that every transcendental entire function f grows transcendentally in a sequence of cercles de remplissage. An example shows that if

formula here

then there may be no sequence of cercles de remplissage the union of which contains infinitely many zeros of f. It is also shown that every transcendental entire function f has a Hayman direction, that is, a direction θ such that, in every open sector containing θ, either f assumes all complex values infinitely often, or else every derivative of f assumes all complex values, except possibly zero, infinitely often.

Type
Notes and Papers
Information
Bulletin of the London Mathematical Society , Volume 31 , Issue 1 , January 1999 , pp. 59 - 66
Copyright
© The London Mathematical Society 1999

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