Exceptional values of differential polynomials

Willibald Doeringer

Vol. 98 (1982), No. 1, 55–62

DOI: 10.2140/pjm.1982.98.55

Abstract

Let f be a meromorphic non-rational function on C and Q[f], P[f] differential polynomials in f. Assuming that neither of them vanishes identically, functions of the form fⁿQ[f] + P[f], n ∈ N, are shown not to have zero as a Picard or Borel exceptional value for sufficiently large n. Examples show that the estimates given for n are optimal.

Mathematical Subject Classification 2000

Primary: 30D35

Secondary: 30C10, 30D30

Milestones

Received: 1 December 1980

Revised: 27 March 1981

Published: 1 January 1982