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Dual Ramanujan-Fourier series

Abstract : 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.
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Submitted on : Friday, December 22, 2017 - 9:41:34 AM
Last modification on : Monday, March 28, 2022 - 8:14:08 AM

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

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