László Tóth: Some remarks on Ramanujan sums and cyclotomic polynomials, p.277-292

Abstract:

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

Key Words: Ramanujan sum, cyclotomic polynomial, Euler's function, Möbius function, divisibility of polynomials.

2000 Mathematics Subject Classification: Primary: 11A25;
Secondary: 11B83, 11C08, 11Y70.

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