Sums of products of Ramanujan sums

Abstract

The Ramanujan sum $c_n(k)$ is defined as the sum of $k$-th powers of the primitive $n$-th roots of unity. We investigate arithmetic functions of $r$ variables defined as certain sums of the products $c_{m_1}(g_1(k))...c_{m_r}(g_r(k))$, where $g_1,...,g_r$ are polynomials with integer coefficients. A modified orthogonality relation of the Ramanujan sums is also derived.

arXiv comment13 pages, revised

References in corpus (1)

• A multivariate arithmetic function of combinatorial and topological significance