Asymptotic behavior of a series of Euler's totient function $\phi (k)$ times the index of $1/k$ in a Farey sequence

R. Tomas

Motivated by studies in accelerator physics this paper computes the asymptotic behavior of the series $\sum _{k=1}^N\phi (k)I_N\left(\frac{1}{k}\right)$, where $\phi (k)$ is…