Tóth, László; Haukkanen, Pentti The discrete Fourier transform of \(r\)-even functions. (English) Zbl 1262.11005 Acta Univ. Sapientiae, Math. 3, No. 1, 5-25 (2011). A function \(f: \mathbb N\to\mathbb C\) is \(r\)-even, if \(f((n,r))= f(n)\) for all \(n\in\mathbb N\). The discrete Fourier transform of such a function is \[ \widehat f(n)= \sum_{k\bmod r} f(k)\exp(-2\pi ikn/r). \] It is again \(r\)-even. The authors study this transformation and gain direct proofs of known properties and results of even functions such as the Ramanujan sums. Reviewer: Jürgen Spilker (Freiburg i. Br.) Cited in 11 Documents MSC: 11A25 Arithmetic functions; related numbers; inversion formulas 11L03 Trigonometric and exponential sums (general theory) 11N37 Asymptotic results on arithmetic functions Keywords:arithmetic functions; even functions; discrete Fourier transform; Ramanujan sums PDFBibTeX XMLCite \textit{L. Tóth} and \textit{P. Haukkanen}, Acta Univ. Sapientiae, Math. 3, No. 1, 5--25 (2011; Zbl 1262.11005) Full Text: arXiv EMIS