[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/CKMS.c150206

THE MINIMAL POLYNOMIAL OF cos(2π/n)

Gurtas, Yusuf Z. (Department of Mathematics and Computer Sciences Queensborough Community College)

Publication Information

Communications of the Korean Mathematical Society / v.31, no.4, 2016 , pp. 667-682 More about this Journal

Abstract

In this article we show a recursive method to compute the coefficients of the minimal polynomial of cos( $2{\pi}/n$ ) explicitly for $n{\geq}3$ . The recursion is not on n but on the coefficient index. Namely, for a given n, we show how to compute ei of the minimal polynomial ${\sum_{i=0}^{d}}(-1)^ie_ix^{d-i}$ for $i{\geq}2$ with initial data $e_0=1$ , $e_1={\mu}(n)/2$ , where ${\mu}(n)$ is the $M{\ddot{o}}bius$ function.

Keywords

minimal polynomial; cyclotomic polynomial; algebraic number; Ramanujan sum; cosine;

Citations & Related Records

Reference

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