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Michael Welter

A new class of integer-valued entire functions

In 1968 Fridman [G. A. Fridman, Entire integer-valued functions, Mat. Sb. (N.S.) 75 (117) (1968), 417–431] found a lower bound for the growth of transcendental entire functions that together with all their derivatives map ? into ?. In this paper we study entire functions that satisfy f ^(? )(n) ? ? for all positive integers n and ? = 0, ? , s_n , where (s_n ) is a sequence of positive integers of exponential growth. As a corollary to our results we get an improvement of Fridman’s lower bound. In the ?nal section we brie?y report on our analogous results in imaginary quadratic number ?elds and for functions that take integer values on a geometric progression.

Journal fur die reine und angewandte Mathematik (Crelles Journal), Walter de Gruyter

Print ISSN: 0075-4102
Volume: 2005, 06/2005
Pages: 175 - 192

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