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Let $$D_n$$ denote the dihedral group of order 2n. We find infinite $$D_6$$ -families and an infinite $$D_3$$ -family of monic irreducible reciprocal sixth-degree polynomials $$f(x)\in \mathbb {Z}[x]$$ , such… Click to show full abstract
Let $$D_n$$ denote the dihedral group of order 2n. We find infinite $$D_6$$ -families and an infinite $$D_3$$ -family of monic irreducible reciprocal sixth-degree polynomials $$f(x)\in \mathbb {Z}[x]$$ , such that $$\{1,\theta ,\theta ^2,\theta ^3,\theta ^4,\theta ^5\}$$ is a basis for the ring of integers of $$L=\mathbb {Q}(\theta )$$ , where $$f(\theta )=0$$ .
Keywords:
dihedral polynomials;
theta theta;
theta;
reciprocal monogenic;
monogenic dihedral;
sextic reciprocal
Journal Title: Ramanujan Journal
Year Published: 2020
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Journal Title: Ramanujan Journal
Year Published: 2020
Link to full text (if available)
Share on Social Media: Sign Up to like & get
recommendations!