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arXiv · 2610.36279

Boundary and Interior of Root Sets of Power Series

Jacob Kewarth
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Abstract

In this paper we study the set $\mathcal{M}_M$ of roots of power series with coefficients in $\{0, \pm 1, ..., \pm M \}$ and constant coefficient $1$. We prove that every nonreal root in the unit disk of a polynomial of this form is an interior point of $\mathcal{M}_M$. Moreover we establish a dimension formula and show the corresponding Hausdorff measure is finite and positive for a family of attractors parameterized by boundary parameters $λ\in \partial \mathcal{M}_M \setminus \mathbb{R}$. Finally we show that $\partial \mathcal{M}_M$ has Lebesgue measure zero.

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Jacob Kewarth. 2026-10-26. Boundary and Interior of Root Sets of Power Series. https://arxiv.org/abs/2610.36279

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