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November 2021 Remarks on the Middle Coefficient of the Cyclotomic Polynomial $\Phi_{3p_2p_3}$
Ala'a Al-Kateeb, Jenan Shtayat
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Missouri J. Math. Sci. 33(2): 214-224 (November 2021). DOI: 10.35834/2021/3302214

Abstract

The middle coefficient of a polynomial of an even degree $d$ is the coefficient of $x^{\frac{d}{2}}$. In this note, we compute the middle coefficient of the cyclotomic polynomial $\Phi_{3p_2p_3}(x)$ when $p_3\equiv \pm 7,\pm 8, \pm10 \mod3p_2$. Also, we compute the middle coefficient of the cyclotomic polynomial $\Phi_{3p_2p_3}(x)$ for some general cases.

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Ala'a Al-Kateeb. Jenan Shtayat. "Remarks on the Middle Coefficient of the Cyclotomic Polynomial $\Phi_{3p_2p_3}$." Missouri J. Math. Sci. 33 (2) 214 - 224, November 2021. https://doi.org/10.35834/2021/3302214

Information

Published: November 2021
First available in Project Euclid: 30 November 2021

Digital Object Identifier: 10.35834/2021/3302214

Subjects:
Primary: 11B83
Secondary: 11C08

Keywords: cyclotomic polynomials , middle coefficient

Rights: Copyright © 2021 University of Central Missouri, School of Computer Science and Mathematics

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Vol.33 • No. 2 • November 2021
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