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 ℕ into ℤ. In this paper we study entire functions that satisfy f (σ )(n) ∈ ℤ for all positive integers n and σ = 0, … , sn , where (sn ) 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 ﬁnal section we brieﬂy report on our analogous results in imaginary quadratic number ﬁelds and for functions that take integer values on a geometric progression.
© Walter de Gruyter