Dual Ramanujan-Fourier series

Noboru Ushiroya (1)

1 National Institute of Technology, Wakayama College

Let cq(n) be the Ramanujan sums. Many results concerning Ramanujan-Fourier series f (n) = ∞ q=1 aqcq(n) are obtained by many mathematicians. In this paper we study series of the form f (q) = ∞ n=1 ancq(n), which we call dual Ramanujan-Fourier series. We extend Lucht's theorem and Delange's theorem to this case and obtain some results.

Mots clés: Ramanujan-Fourier series; Ramanujan sums; arithmetic functions; multiplicative functions 2010

Domaines: Mathématiques [math]

Noboru Ushiroya. Dual Ramanujan-Fourier series. Hardy-Ramanujan Journal, 2018, Volume 40 - 2017, pp.1-23. ⟨10.46298/hrj.2018.2541⟩. ⟨hal-01671222⟩