Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Discrete Fourier Transform of $\mathbf{(r,s)-}$even functions   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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The categories of this paper are: q-bio
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The categories of this paper are: nucl-ex
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The categories of this paper are: q-alg
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The categories of this paper are: patt-sol
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-th
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: supr-con
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The categories of this paper are: mtrl-th
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The categories of this paper are: gr-qc
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The categories of this paper are: alg-geom
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The categories of this paper are: nucl-th
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The categories of this paper are: adap-org
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The categories of this paper are: physics
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The categories of this paper are: math-ph