Vol. 96, No. 1, 1981

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Imaginary values of meromorphic functions in the disk

Douglas Wayne Townsend

Vol. 96 (1981), No. 1, 225–242
Abstract

Let f be a meromorphic function in the unit disk, and let ϕ(r,f) be the number of solutions of the equation Re f(rei𝜃) = 0 for 0 𝜃 2π. In this paper we bound ϕ(r,f) off an exceptional set of r values, and Φ(r,f) = 0rϕ(t,f)(1 t)1 dt for all r, in terms of the Nevanlinna characteristic function of f. We then give examples to show that the bounds obtained are the best possible.

Mathematical Subject Classification 2000
Primary: 30D35
Secondary: 30D30
Milestones
Received: 31 May 1978
Revised: 30 May 1980
Published: 1 September 1981
Authors
Douglas Wayne Townsend