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arXiv · 1710.01679

The asymptotic zero-counting measure of iterated derivaties of a class of meromorphic functions

Christian Hägg
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Abstract

We give an explicit formula for the logarithmic potential of the asymptotic zero-counting measure of the sequence $\left\{\frac{\mathrm{d}^n}{\mathrm{d}z^n}\left(R(z)\exp{T(z)}\right)\right\}$. Here, $R(z)$ is a rational function with at least two poles, all of which are distinct, and $T(z)$ is a polynomial. This is an extension of a recent measure-theoretic refinement of P\'olya's Shire theorem for rational functions.

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Christian Hägg. 2017-10-04. The asymptotic zero-counting measure of iterated derivaties of a class of meromorphic functions. https://arxiv.org/abs/1710.01679

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