Expansions of arithmetic functions of several variables with respect to certain modified unitary Ramanujan sums

zbMATH Open1449.11010arXiv1705.01363MaRDI QIDQ4685151

László Tóth

Publication date: 5 October 2018

Abstract: We introduce new analogues of the Ramanujan sums, denoted by $widetilde{c}_q(n)$, associated with unitary divisors, and obtain results concerning the expansions of arithmetic functions of several variables with respect to the sums $widetilde{c}_q(n)$. We apply these results to certain functions associated with $sigm{a}^{*}(n)$ and $ph{i}^{*}(n)$, representing the unitary sigma function and unitary phi function, respectively.

Full work available at URL: https://arxiv.org/abs/1705.01363

zbMATH Keywords

multiplicative functionunitary divisorarithmetic function of several variablessum of unitary divisorsRamanujan expansion of arithmetic functionsunitary Ramanujan sumunitary Euler function

Mathematics Subject Classification ID

Asymptotic results on arithmetic functions (11N37) Arithmetic functions; related numbers; inversion formulas (11A25)

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