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arXiv · 1104.1906

Sums of products of Ramanujan sums

László Tóth
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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.

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László Tóth. 2012-07-17. Sums of products of Ramanujan sums. https://doi.org/10.1007/s11565-011-0143-3

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