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

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 Hölder identity. We also use DFT to give shorter proofs of certain well known results and identities .

To appear in the Indian Journal of Pure and Applied Mathematics

References in corpus (2)

• Discrete Ramanujan-Fourier Transform of Even Functions (mod $r$)
• On solving a restricted linear congruence using generalized Ramanujan sums

Cited by in corpus (1)

• On the number of solutions of a restricted linear congruence