Year: 2025
Type: preprint
Abstract: We treat shared value problems for rational functions $R(z)$ and their derivative $R'(z)$ in the plane and on the sphere. We also consider shared values for the pair $R(w)$ and $\partial_{z} R = λw \cdot R'(w)$ on ${\mathbb C} \setminus \{ 0 \}$ and $\widehat{\mathbb C}$, again with rational functions $R$. In ${\mathbb C} \setminus \{ 0 \}$ this is related to shared values of meromorphic functions $f : {\mathbb C} \to \widehat{\mathbb C}$ and $f'$ through $f(z)=R(w)$ with $w=\exp(λz)$, while on $\widehat{\mathbb C}$ this is connected to shared limit values in a similar fashion.
Source: arXiv (Cornell University)
Authors: Sauer, Andreas, Schweizer, Andreas
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4417070255
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