Rocky Mountain Journal of Mathematics

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

Alaa Al-Kateeb

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

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


Export citation

References

  • A. Al-Kateeb, Structures and properties of cyclotomic polynomials, Ph.D. thesis, North Carolina State University (2016).
  • A.S. Bang, Om Ligningen $\phi_n(x) = 0$, Nyt Tidsskr. Math. 6 (1895), 6–12.
  • M. Beiter, Coefficients of the cyclotomic polynomial $F_{3qr} (x)$, Fibonacci Quart. 16 (1978), 302–306.
  • G. Dresden, On the middle coefficient of a cyclotomic polynomial, Amer. Math. Monthly 111 (2004), no. 6, 531–533.
  • T.Y. Lam and K.H. Leung, On the cyclotomic polynomial $\Phi_{pq} (X)$, Amer. Math. Monthly 103 (1996), no. 7, 562–564.
  • M. Beiter, The midterm coefficient of the cyclotomic polynomial $F_{pq}(x)$, Amer. Math. Monthly 71 (1964), no. 7, 769–770.
  • R. Thangadurai, On the coefficients of cyclotomic polynomials, pp. 311–322 in Cyclotomic fields and related topics (Pune, 1999), Bhaskaracharya Pratishthana, Pune (2000).