Remarks on generalized Ramanujan sums and even functions

Details Remarks on generalized Ramanujan sums and even functions Remarks on generalized Ramanujan sums and even functions

2006-10-11

arxiv.org/abs/math/0610358v1

Acta Math. Acad. Paedagog. Nyh\'azi. (N. S.), electronic, 20 (2004), 233-238

Mathematics

Number Theory

Scientific paper

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 $c(n,r)$.

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