Some remarks about the minimal polynomials of $4{\sin ^2}\left( {\frac{π}{n}} \right)$

We show that the values of the minimal polynomials ${ϕ_n}(x)$ of $4{\sin ^2}\left( {\frac{π}{n}} \right)$ for $x \in \left\{ {0,1,2,3,4} \right\}$ are intimately related to the prime factorization of $n.$

Publication Details

Journal
ArXiv.org
Published
2025-03-25
Primary Topic
Analytic Number Theory Research
Type
article
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article

Some remarks about the minimal polynomials of $4{\sin ^2}\left( {\frac{π}{n}} \right)$

ArXiv.org
Analytic Number Theory Research
article

Some remarks about the minimal polynomials of $4{\sin ^2}\left( {\frac{π}{n}} \right)$

article en

Abstract

We show that the values of the minimal polynomials ${ϕ_n}(x)$ of $4{\sin ^2}\left( {\frac{π}{n}} \right)$ for $x \in \left\{ {0,1,2,3,4} \right\}$ are intimately related to the prime factorization of $n.$

ArXiv.org
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Analytic Number Theory Research
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Some remarks about the minimal polynomials of $4{\sin ^2}\left( {\frac{π}{n}} \right)$ · ArXiv.org (2025) | TGRS Research Map | TGRS