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arXiv · 1702.07650

Lower Bounds for Maximum Gap in (Inverse) Cyclotomic Polynomials

Mary Ambrosino·Hoon Hong·Eunjeong Lee
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Abstract

The maximum gap $g(f)$ of a polynomial $f$ is the maximum of the differences (gaps) between two consecutive exponents that appear in $f$. Let $\Phi_{n}$ and $\Psi_{n}$ denote the $n$-th cyclotomic and $n$-th inverse cyclotomic polynomial, respectively. In this paper, we give several lower bounds for $g(\Phi_{n})$ and $g(\Psi_{n})$, where $n$ is the product of odd primes. We observe that they are very often exact. We also give an exact expression for $g(\Psi_{n})$ under a certain condition. Finally we conjecture an exact expression for $g(\Phi_{n})$ under a certain condition.

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Mary Ambrosino, Hoon Hong, Eunjeong Lee. 2017-02-24. Lower Bounds for Maximum Gap in (Inverse) Cyclotomic Polynomials. https://arxiv.org/abs/1702.07650

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