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Cercles De Remplissage for Entire Functions
Author(s) -
Fenton P. C.,
Rossi John
Publication year - 1999
Publication title -
bulletin of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.396
H-Index - 48
eISSN - 1469-2120
pISSN - 0024-6093
DOI - 10.1112/s0024609398004834
Subject(s) - transcendental number , mathematics , entire function , sequence (biology) , combinatorics , zero (linguistics) , function (biology) , pure mathematics , mathematical analysis , philosophy , genetics , evolutionary biology , biology , linguistics
It is shown that every transcendental entire function f grows transcendentally in a sequence of cercles de remplissage . An example shows that iflim r → ∞¯ log M ( r , f ) /( log r ) 2 = ∞ ,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. 1991 Mathematics Subject Classification 30D20.