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arXiv · 2504.19336

The sequence of partial sums of a unimodular power series is not ultraflat

Tamás Erdélyi
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Abstract

We show that if $(a_j)_{j=0}^\infty$ is a sequence of numbers $a_j \in {\Bbb C}$ with $|a_j|=1$, and $$P_n(z) = \sum_{j=0}^n{a_jz^j}\,, \qquad n=0,1,2,\ldots\,,$$ then $(P_n)$ is NOT an ultraflat sequence of unimodular polynomials. This answers a question raised by Zachary Chase.

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Tamás Erdélyi. 2025-04-27. The sequence of partial sums of a unimodular power series is not ultraflat. https://arxiv.org/abs/2504.19336

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