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Dual Ramanujan-Fourier series
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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.
Centre pour la Communication Scientifique Directe (CCSD)
Title: Dual Ramanujan-Fourier series
Description:
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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