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arXiv · 2401.13808

Maximum and average valence of meromorphic functions

Aimo Hinkkanen·Joseph Miles
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Abstract

If $f$ is a meromorphic function from the complex plane ${\mathbb C}$ to the extended complex plane $\overline{ {\mathbb C} }$, for $r > 0$ let $n(r)$ be the maximum number of solutions in $\{z\colon |z| \leq r \}$ of $f(z) = a$ for $a \in \overline{ {\mathbb C} }$, and let $A(r,f)$ be the average number of such solutions. Using a technique introduced by Toppila, we exhibit a meromorphic function for which $\liminf_{r\to\infty} n(r)/A(r,f) \geq 1.07328$.

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Aimo Hinkkanen, Joseph Miles. 2024-01-24. Maximum and average valence of meromorphic functions. https://arxiv.org/abs/2401.13808

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