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Sums of products of Ramanujan sums

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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 \({c_{m_1}(g_1(k))\cdots c_{m_r}(g_r(k))}\), 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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Authors and Affiliations

  1. Department of Mathematics, University of Pécs, Ifjúság u. 6, Pécs, 7624, Hungary

    László Tóth

  2. Department of Integrative Biology, Institute of Mathematics, Universität für Bodenkultur, Gregor Mendel-Straße 33, 1180, Wien, Austria

    László Tóth

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  1. László Tóth
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Correspondence to László Tóth.

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The author gratefully acknowledges support from the Austrian Science Fund (FWF) under the project Nr. P20847-N18.

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Tóth, L. Sums of products of Ramanujan sums. Ann Univ Ferrara 58, 183–197 (2012). https://doi.org/10.1007/s11565-011-0143-3

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  • DOI: https://doi.org/10.1007/s11565-011-0143-3

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