The image of Carmichael's $\lambda$-function

TL;DR

This paper investigates the distribution of values of Carmichael's lambda function, revealing that its counting function grows approximately as x divided by a power of log x, with a specific constant exponent.

Contribution

The paper provides an asymptotic estimate for the counting function of Carmichael's lambda function values, a novel result in understanding its distribution.

Findings

Counting function grows as x/(log x)^{η+o(1)}

Explicit constant η=0.08607...

Advances knowledge of Carmichael's lambda function distribution

Abstract

We show that the counting function of the set of values of the Carmichael $\lambda$-function is $x/(\log x)^{\eta+o(1)}$, where $\eta=1-(1+\log\log 2)/(\log 2)=0.08607...$.