The Discrete Fourier Transform of (r, s)-Even Functions

K. Vishnu Namboothiri ()
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K. Vishnu Namboothiri: Government College, Ambalapuzha, Alappuzha

Indian Journal of Pure and Applied Mathematics, 2019, vol. 50, issue 1, 253-268

Abstract: 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.

Keywords: Periodic functions; (r; s)-even functions; multiplicative functions; discrete Fourier transform; generalized Ramanujan sum; linear congruences; Hölder’s identity (search for similar items in EconPapers)
Date: 2019
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DOI: 10.1007/s13226-019-0322-y

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