SEMI-CYCLOTOMIC POLYNOMIALS

• Journal title : Honam Mathematical Journal
• Volume 37, Issue 4,  2015, pp.469-472
• Publisher : The Honam Mathematical Society
• DOI : 10.5831/HMJ.2015.37.4.469
Title & Authors
SEMI-CYCLOTOMIC POLYNOMIALS
LEE, KI-SUK; LEE, JI-EUN; Kim, JI-HYE;

Abstract
The n-th cyclotomic polynomial $\small{{\Phi}_n(x)}$ is irreducible over $\small{\mathbb{Q}}$ and has integer coefficients. The degree of $\small{{\Phi}_n(x)}$ is $\small{{\varphi}(n)}$, where $\small{{\varphi}(n)}$ is the Euler Phi-function. In this paper, we define Semi-Cyclotomic Polynomial $\small{J_n(x)}$. $\small{J_n(x)}$ is also irreducible over $\small{\mathbb{Q}}$ and has integer coefficients. But the degree of $\small{J_n(x)}$ is $\small{\frac{{\varphi}(n)}{2}}$. Galois Theory will be used to prove the above properties of $\small{J_n(x)}$.
Keywords
n-th cyclotomic polynomial;semi-cyclotomic polynomial;irreducible polynomial;
Language
English
Cited by
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