Dual Ramanujan-Fourier series

Noboru Ushiroya

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arXiv · 1611.06630

Dual Ramanujan-Fourier series

Noboru Ushiroya

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Abstract

Let $c_q(n)$ be the Ramanujan sums. Many results concerning Ramanujan-Fourier series $f(n)=\sum_{q=1}^\infty a_q c_q (n)$ are obtained by many mathematicians. In this paper we study series of the form $f(q)=\sum_{n=1}^\infty a_n c_q (n)$, which we call dual Ramanujan-Fourier series. We extend Lucht's theorem and Delange's theorem to this case and obtain some results.

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Noboru Ushiroya. 2016-11-21. Dual Ramanujan-Fourier series. https://arxiv.org/abs/1611.06630

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