Dual Ramanujan-Fourier series

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.

arXiv comment23 pages