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

Tóth, László (2014) Averages of Ramanujan sums: note on two papers by E. Alkan. RAMANUJAN JOURNAL, 35 (1). pp. 149-156. ISSN 1382-4090

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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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