## Ushiroya, Noboru - Dual Ramanujan-Fourier series

hrj:2541 - Hardy-Ramanujan Journal, January 11, 2018, Volume 40
Dual Ramanujan-Fourier series

Authors: Ushiroya, Noboru

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.

Source : oai:arXiv.org:1611.06630
Volume: Volume 40
Published on: January 11, 2018
Submitted on: November 22, 2016
Keywords: Mathematics - Number Theory,11A25, 11N37