Effective finiteness of solutions to certain differential and difference equations
نویسندگان
چکیده
Abstract For $R(z, w)\in \mathbb {C}(z, w)$ of degree at least 2 in w , we show that the number rational functions $f(z)\in {C}(z)$ solving difference equation $f(z+1)=R(z, f(z))$ is finite and bounded just terms degrees R two variables. This complements a result Yanagihara, who showed any finite-order meromorphic solution to this sort must be function. We prove similar for differential $f'(z)=R(z, building on Eremenko.
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ژورنال
عنوان ژورنال: Canadian mathematical bulletin
سال: 2021
ISSN: ['1496-4287', '0008-4395']
DOI: https://doi.org/10.4153/s0008439521000072