Some remarks on Ramanujan sums and cyclotomic polynomials

Abstract

We investigate the polynomials ${\sum }_{k=0}^{n-1}{c}_n(k)x^k$ and ${\sum }_{k=0}^{n-1}|c_n(k)|x^k$, where $c_n(k)$ denote the Ramanujan sums. We point out connections and analogies to the cyclotomic polynomials.

14 pages