Annales Academię Scientiarum Fennicę

Mathematica

Volumen 34, 2009, 615-636

# MEROMORPHIC COMPOSITIONS AND TARGET FUNCTIONS

## Alastair N. Fletcher and James K. Langley

University of Glasgow, Department of Mathematics

University Gardens, Glasgow
G12 8QW, United Kingdom; a.fletcher 'at' maths.gla.ac.uk

University of Nottingham, School of Mathematical Sciences

University Park, Nottingham NG7 2RD, United Kingdom; jkl 'at' maths.nott.ac.uk

**Abstract.**
We prove a result on the frequency
of zeros of *f* o *g* - *Q*, where *g* is a transcendental entire function
of finite lower order, and *f* and
*Q* are meromorphic functions in the plane such that
*f* has finite order and the growth of the target function
*Q* is controlled by that of *g*. The particular case *f* = *Q* is then
investigated further.

**2000 Mathematics Subject Classification:**
Primary 30D35.

**Key words:**
Meromorphic functions, compositions,
Nevanlinna theory.

**Reference to this article:** A.N. Fletcher and J.K. Langley:
Meromorphic compositions and target functions
Ann. Acad. Sci. Fenn. Math. 34 (2009), 615-636.

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Copyright © 2009 by Academia Scientiarum Fennica