A class of Julia exceptional functions

V. S. Khoroshchak, A. Ya. Khrystiyanyn, D. V. Lukivska

Abstract


The class of $p$-loxodromic functions (meromorphic functions, satisfying the condition $f(qz) = pf(z)$ for some $q \in \mathbb{C}\backslash \{0\}$ and all $z \in \mathbb{C}\backslash \{0\}$) is studied. Each $p$-loxodromic function is Julia exceptional. The representation of these functions as well as their zero and pole distribution are investigated.


Keywords


$p$-loxodromic function, the Schottky-Klein prime function, Julia exceptionality

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