Abstract
An (r, s)-even function is a special type of periodic function mod rs. These functions were defined and studied for the the first time by McCarthy. An important example for such a function is a generalization of Ramanujan sum defined by Cohen. In this paper, we give a detailed analysis of DFT of (r, s)-even functions and use it to prove some interesting results including a generalization of the Hölder identity. We also use DFT to give shorter proofs of certain well known results and identities.
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Namboothiri, K.V. The Discrete Fourier Transform of (r, s)-Even Functions. Indian J Pure Appl Math 50, 253–268 (2019). https://doi.org/10.1007/s13226-019-0322-y
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DOI: https://doi.org/10.1007/s13226-019-0322-y