The discrete Fourier transform of $r$-even functions

Details The discrete Fourier transform of $r$-even functions The discrete Fourier transform of $r$-even functions

2010-09-27

arxiv.org/abs/1009.5281v1

Acta Univ. Sapientiae, Math. 3 (2011), 5--25

Mathematics

Number Theory

15 pages

Scientific paper

We give a detailed study of the discrete Fourier transform (DFT) of $r$-even arithmetic functions, which form a subspace of the space of $r$-periodic arithmetic functions. We consider the DFT of sequences of $r$-even functions, their mean values and Dirichlet series. Our results generalize properties of the Ramanujan sum. We show that some known properties of $r$-even functions and of the Ramanujan sum can be obtained in a simple manner via the DFT.

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