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arXiv · 1708.04507

The Discrete Fourier Transform of $\mathbf{(r,s)-}$even functions

K Vishnu Namboothiri
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Abstract

An $(r,s)$-even function is a special type of periodic function mod $r^s$. 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 H\"{o}lder identity. We also use DFT to give shorter proofs of certain well known results and identities .

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K Vishnu Namboothiri. 2017-08-15. The Discrete Fourier Transform of $\mathbf{(r,s)-}$even functions. https://arxiv.org/abs/1708.04507

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