The Asymptotic Behavior of Compositions of the Euler and Carmichael Functions

2012/06/01 by Vishaal Kapoor, Kapoor, Vishaal
Mathematics · #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1206.0286

18 pages, 2 figures

arxiv created 2012/06/01 · arxiv updated 2012/06/04

Abstract

We compare the asymptotic behavior of Carmichael's lambda function composed with Euler's totient function to the asymptotic behavior of Carmichael's lambda function composed with itself. We establish the normal order of the logarithm of the ratio.

Related

• The iterated Carmichael lambda function
• On two functions arising in the study of the Euler and Carmichael quotients
• The number of iterates of the Carmichael lambda function required to reach 1
• Asymptotic formulas for the logarithm of general L-functions at and near s=1
• A relation to a remainder terms in an asymptotic formula for the associated Euler totient function