Meromorphic functions with negative zeros and positive poles and a theorem of Teichmuller

Jack Williamson

Vol. 42 (1972), No. 3, 795–810

DOI: 10.2140/pjm.1972.42.795

Abstract

Let ℳ_λ denote the class of meromorphic functions of finite order λ whose zeros lie on the negative real axis and whose poles lie on the positive real axis. Let 𝒯_λ denote the class of functions belonging to ℳ_λ whose zeros and poles are symmetrically located along the real axis.

In the study of certain aspects of the value distribution properties of meromorphic functions of order λ < 1, the class ℳ_λ,λ < 1, has receiitly been found to display certain striking and useful extremal properties, while earlier results on the subclass 𝒯_λ,λ < 1, have been important as a guide to the possible values of their Nevanlinna deficiencies. In this note the class 𝒯_λ,λ > 1, is studied and it is concluded that certain extremal properties displayed by ℳ_λ for λ < 1 do not extend to the case λ > 1.

Mathematical Subject Classification

Primary: 30A70

Milestones

Received: 4 September 1970

Revised: 24 June 1971

Published: 1 September 1972