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MODIFIED CYCLOTOMIC POLYNOMIALS

Taehan Suhakhoe hoebo, 2022-11, Vol.59 (6), p.1511-1522 [Peer Reviewed Journal]

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Title:
MODIFIED CYCLOTOMIC POLYNOMIALS
Author: Ae-Kyoung, Cha ; Miyeon, Kwon ; Ki-Suk, Lee ; Seong-Mo, Yang
Is Part Of: Taehan Suhakhoe hoebo, 2022-11, Vol.59 (6), p.1511-1522
Description: Let H be a subgroup of $\mathbb{Z}^*_n$ (the multiplicative group of integers modulo n) and h1, h2, ..., hl distinct representatives of the cosets of H in $\mathbb{Z}^*_n$. We now define a polynomial Jn,H(x) to be _{n,H}(x)=\prod^l_{j=1} \left( x-\sum_{h{\in}H} {\zeta}^{h_jh}_n\right) where ${\zeta}_n=e^{\frac{2{\pi}i}{n}}$ is the nth primitive root of unity. Polynomials of such form generalize the nth cyclotomic polynomial $\Phi_n(x)={\prod}_{k{\in}\mathbb{Z}^*_n}(x-{\zeta}^k_n)$ as Jn,{1}(x) = Φn(x). While the nth cyclotomic polynomial Φn(x) is irreducible over ℚ, Jn,H(x) is not necessarily irreducible. In this paper, we determine the subgroups H for which Jn,H(x) is irreducible over ℚ.
Language: Korean
Identifier: ISSN: 1015-8634
DOI: 10.4134/BKMS.b210864
Source: Alma/SFX Local Collection

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