DDT theorem over $k$-free numbers in short intervals

Czechoslovak Mathematical Journal 2026

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Authors: Ruiyang Liu, Tingting Wen
DOI: 10.21136/cmj.2026.0382-25
Cited by: 0

Abstract

summary:Let $k\geq 3$ be an integer. We investigate the distribution of divisors of $k$-free numbers using the Selberg-Delange method. We establish that the Cesàro mean of distribution functions converges uniformly to the arcsine law in short intervals. This generalizes the Deshouillers-Dress-Tenenbaum (DDT) theorem.

Fields of Study & Subjects

Analytic Number Theory Research Limits and Structures in Graph Theory Probability and Statistical Research

Publication details

Journal / source
Czechoslovak Mathematical Journal
Volume
76
Issue
1
Pages
335–347
Publication date
27 February 2026
Language
EN