Annales Academiæ Scientiarum Fennicæ

Mathematica

Volumen 32, 2007, 151-170

# ON A CLASS OF COMPLEX FUNCTIONAL EQUATIONS

## Jarkko Rieppo

University of Joensuu, Department of Physics and Mathematics

P.O. Box 111, FI-80101 Joensuu, Finland; jarkko.rieppo 'at' jns.fi

**Abstract.**
We consider a class of complex functional equations that admit
transcendental meromorphic solutions with
relatively few distinct poles. The solutions are characterized
and it is shown that they must also satisfy a functional equation of the
certain simple form. The equations that are considered contains
e.g. some delay equations and the generalized Schröder
equation as special cases. The reasoning relies on the combination
of Nevanlinna theory and algebraic field theory.

**2000 Mathematics Subject Classification:**
Primary 30D05; Secondary 30D35, 39B32.

**Key words:**
Complex functional equation, Schröder equation, hypertranscendency,
Nevanlinna theory, value distribution theory.

**Reference to this article:** J. Rieppo:
On a class of complex functional equations.
Ann. Acad. Sci. Fenn. Math. 32 (2007), 151-170.

Full document as PDF file

Copyright © 2007 by Academia Scientiarum Fennica