On the growth of meromorphic functions with radially distributed zeros and poles

Joseph B. Miles

Vol. 122 (1986), No. 1, 147–167

DOI: 10.2140/pjm.1986.122.147

Abstract

The lowest possible rate of growth of a meromorphic function f of genus q with zeros and poles restricted to a given finite set of rays through the origin is determined in terms of q and the rays carrying the zeros and poles. For α > 1 the ratio T(αr,f)∕T(r,f) is shown to be bounded as r tends to infinity for all such entire functions, but not for all such meromorphic functions.

Mathematical Subject Classification 2000

Primary: 30D35

Secondary: 30D15

Milestones

Received: 5 September 1984

Published: 1 March 1986