Rocky Mountain Journal of Mathematics

On the middle coefficient of $\Phi _{3p_2p_3}$

Alaa Al-Kateeb

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Abstract

The middle coefficient of a polynomial of an even degree $d$ is the coefficient of $x^{{d}/{2}}$. In this note we compute the middle coefficient of the cyclotomic polynomial $\Phi _{3p_2p_3}(x)$ when $p_3\equiv \pm 2,\pm 4, \pm 5\bmod 3p_2$.

Article information

Source
Rocky Mountain J. Math., Volume 49, Number 6 (2019), 1755-1767.

Dates
First available in Project Euclid: 3 November 2019

Permanent link to this document
https://projecteuclid.org/euclid.rmjm/1572746416

Digital Object Identifier
doi:10.1216/RMJ-2019-49-6-1755

Mathematical Reviews number (MathSciNet)
MR4027231

Subjects
Primary: 11B83: Special sequences and polynomials
Secondary: 11C08: Polynomials [See also 13F20] 11N56: Rate of growth of arithmetic functions

Keywords
Cyclotomic polynomials middle coefficient

Citation

Al-Kateeb, Alaa. On the middle coefficient of $\Phi _{3p_2p_3}$. Rocky Mountain J. Math. 49 (2019), no. 6, 1755--1767. doi:10.1216/RMJ-2019-49-6-1755. https://projecteuclid.org/euclid.rmjm/1572746416


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References

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    Mathematical Reviews (MathSciNet): MR3653750
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    Zentralblatt MATH: 0396.10006
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    Zentralblatt MATH: 1062.11016
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