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3rd International ISAAC Congress
August 20-25, 2001
Freie Universitaet Berlin
Berlin, Germany

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Meromorphic functions that satisfy some functional equations
by
Katsuya Ishizaki
Department of Mathematics, Nippon Institute of Technology, 4-1 Gakuendai Miyashiro Minamisaitama Saitama 345-8501, Japan

Wittich [3] proved that a transcendental entire function that satisfies a q-difference equation f(sz)=a(z)f(z)+b(z), where s is a complex number |s| > 1, and a( =/= 0), b are polynomials, does not satisfy any algebraic differential questions. In this talk, we [1] discuss meromorphic solutions of linear q-difference equation of the form \Sigmanj=oaj(z)f(qjz)=0, where |q|=1 is a complex number, aj, j=0, ..., n (ana0 =/= 0) are rational functions. We also mention Ramis' question [2], whether there exists a meromorphic function that satisfies a q-difference equation and a linear differential equation with rational coefficients.

References
[1] Ishizaki, K., T. Sato, M. Suzuki, and N. Yanagihara, q-difference equations and other equations, Preprint.
[2] Ramis, J.-P., About the growth of entire functions solutions of linear algebraic q-difference equations, Annales Fc. Sci. Toulouse, Ser. 6 I (1992), 53-94.
[3] Wittich, H., Bemerkung zu einer Funktionalgleichungen von H. Poincaré, Arch. Math. 2 (1949/1950), 90-95.

Date received: May 16, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahk-59.