The asymptotic distribution of the largest prime divisor

2008/11/19 by Arie Leizarowitz, Leizarowitz, Arie
Mathematics · #11N45 #11N99 #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11N45 #msc:11N99

paper · pdf · doi:10.48550/arxiv.0811.3151

35 p

arxiv created 2008/11/19 · openalex publication_date 2008/11/19 · arxiv updated 2012/03/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Dickman function Ψ(x,y) in the limit when ln x/ln y→ ∞ and ln ln x ln y→ 0. The asymptotic value is expressed in terms of the ratio of iterated loragithm of x and ln y.

Related

• Iterated logarithm approximations to the distribution of the largest prime divisor
• Dickman polylogarithms and their constants
• Popular values of the largest prime divisor function
• A generalization on the average ratio of the smallest and largest prime divisor of n
• Dickman multiple polylogarithms and the Lindemann-Furry letters