Vol. 29, No. 1, 1969

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Bounds for the number of deficient values of entire functions whose zeros have angular densities

Ki-Choul Oum

Vol. 29 (1969), No. 1, 187–202

Let f(z) be an entire function of finite order λ. Arakeljan has shown that, for every λ > 12, f(z) may have infinitely many deficient values in the sense of R. Nevanlinna. We prove here that this cannot happen if (i) the zeros of f(z) have an angular density (in the sense of Pfluger and Levin) and (ii) λ is not an integer. Under these two assumptions the number of deficient values cannot exceed 2λ + 1. If f(z) is of completely regular growth (in the sense of Levin), the result also holds for integral values of the order.

Mathematical Subject Classification
Primary: 30.61
Received: 22 April 1968
Published: 1 April 1969
Ki-Choul Oum