Imaginary values of meromorphic functions in the disk

Douglas W. Townsend

Type: Article

Publication Date: 1981-09-01

Citations: 21

DOI: https://doi.org/10.2140/pjm.1981.96.225

Abstract

Let / be a meromorphic function in the unit disk, and let Φ(r,f) be the number of solutions of the equation Re f(re iθ ) = 0 f or 0 ^ θ ^ 2π.In this paper we bound φ{r, f) off S r Φ(t, /)(1t)~1dt 0 for all r, in terms of the Nevanlinna characteristic function of /.We then give examples to show that the bounds obtained are the best possible.

Locations

Pacific Journal of Mathematics - View - PDF

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