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arXiv · 1305.6018

Averages of Ramanujan sums: Note on two papers by E. Alkan

László Tóth
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Abstract

We give a simple proof and a multivariable generalization of an identity due to E. Alkan concerning a weighted average of the Ramanujan sums. We deduce identities for other weighted averages of the Ramanujan sums with weights concerning logarithms, values of arithmetic functions for gcd's, the Gamma function, the Bernoulli polynomials, and binomial coefficients.

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László Tóth. 2014-09-21. Averages of Ramanujan sums: Note on two papers by E. Alkan. https://doi.org/10.1007/s11139-014-9577-4

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