Sums of products of Ramanujan sums

Details Sums of products of Ramanujan sums Sums of products of Ramanujan sums

2011-04-11

arxiv.org/abs/1104.1906v1

Mathematics

Number Theory

12 pages

Scientific paper

We investigate arithmetical functions of $r$ variables defined as certain
sums of the products $c_{m_1}(g_1(k))... c_{m_r}(g_r(k))$, where $c_n(\ell)$
denote the Ramanujan sums and $g_1,..., g_r$ are polynomials with integer
coefficients. A modified orthogonality relation of the Ramanujan sums is also
derived.

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