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

作者：Toth Laszlo^*

来源：Ramanujan Journal, 2014, 35(1): 149-156.

DOI：10.1007/s11139-014-9577-4

• Ramanujan%26apos
• s sum
• Jordan%26apos
• s function
• Bernoulli numbers and polynomials
• Gamma function

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%26apos;s, the Gamma function, the Bernoulli polynomials, and binomial coefficients.

• 出版日期2014-10