Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 20, No. 2, pp. 233-238 (2004)

Remarks on generalized Ramanujan sums and even functions

L. Tóth

University of Pécs

Abstract: We prove a simple formula for the main value of $r$-even functions and give applications of it. Considering the generalized Ramanujan sums $c_A(n,r)$ involving regular systems $A$ of divisors we show that it is not possible to develop a Fourier theory with respect to $c_A(n,r)$, like in the the usual case of classical Ramanujan sums $c(n,r)$.

Keywords: Ramanujan sum, r-even function, mean value, regular system of divisors.

Classification (MSC2000): 11A25

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