Exponential Carmichael function

Abstract

Consider exponential Carmichael function ${\lambda }^{(e)}$ such that ${\lambda }^{(e)}$ is multiplicative and ${\lambda }^{(e)}(p^a)=\lambda (a)$, where $\lambda$ is usual Carmichael function. We discuss the value of $\sum {\lambda }^{(e)}(n)$, where $n$ runs over certain subsets of $[1,x]$, and provide bounds on the error term, using analytic methods and especially estimates of ${\int }_1^T|\zeta (\sigma +it){|}^{m}dt$.

9 pages