Article contents
Effective finiteness of solutions to certain differential and difference equations
Published online by Cambridge University Press: 16 February 2021
Abstract
For $R(z, w)\in \mathbb {C}(z, w)$ of degree at least 2 in w, we show that the number of rational functions $f(z)\in \mathbb {C}(z)$ solving the difference equation $f(z+1)=R(z, f(z))$ is finite and bounded just in terms of the degrees of R in the two variables. This complements a result of Yanagihara, who showed that any finite-order meromorphic solution to this sort of difference equation must be a rational function. We prove a similar result for the differential equation $f'(z)=R(z, f(z))$ , building on a result of Eremenko.
MSC classification
- Type
- Article
- Information
- Copyright
- © Canadian Mathematical Society 2021
References
- 1
- Cited by