Noboru Ushiroya - Dual Ramanujan-Fourier series

hrj:2541 - Hardy-Ramanujan Journal, January 11, 2018, Volume 40 - 2017 - https://doi.org/10.46298/hrj.2018.2541
Dual Ramanujan-Fourier series

Authors: Noboru Ushiroya

    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.

    https://doi.org/10.46298/hrj.2018.2541
    Source : oai:HAL:hal-01671222v1
    Volume: Volume 40 - 2017
    Published on: January 11, 2018
    Accepted on: November 3, 2017
    Submitted on: November 22, 2016
    Keywords: Ramanujan-Fourier series,Ramanujan sums,arithmetic functions,multiplicative functions 2010,MSC : 11A25, 11N37, [ MATH ] Mathematics [math]

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