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| Main Author: | |
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| Format: | Preprint |
| Published: |
2025
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2504.19336 |
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| _version_ | 1866909595783397376 |
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| author | Erdélyi, Tamás |
| author_facet | Erdélyi, Tamás |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2504_19336 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The sequence of partial sums of a unimodular power series is not ultraflat Erdélyi, Tamás Number Theory 11C08, 41A17 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. |
| title | The sequence of partial sums of a unimodular power series is not ultraflat |
| topic | Number Theory 11C08, 41A17 |
| url | https://arxiv.org/abs/2504.19336 |