Abstract
We derive certain identities involving various known arithmetical functions and a generalized version of Ramanujan sum. L. Tóth constructed certain weighted averages of Ramanujan sums with various arithmetic functions as weights. We choose a generalization of Ramanujan sum given by E. Cohen and derive the weighted averages corresponding to the versions of the weighted averages established by Tóth.
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The author acknowledges the support from the University Grants Commission of India under its Minor Research Project Grant scheme (XII Plan).
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Namboothiri, K.V. Certain weighted averages of generalized Ramanujan sums. Ramanujan J 44, 531–547 (2017). https://doi.org/10.1007/s11139-016-9827-8
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DOI: https://doi.org/10.1007/s11139-016-9827-8
Keywords
- Generalized Ramanujan sum
- Weighted averages
- Jordan totient function
- Gamma function
- Bernoulli numbers
- Holder evaluation