Moments of the distribution of k-free numbers in short intervals and arithmetic progressions

2020/10/08 by Ramon M. Nunes, Nunes, Ramon M. · 1 citation
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematical Dynamics and Fractals #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2010.03696

openalex publication_date 2020/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We show estimates for the distribution of k-free numbers in short intervals and arithmetic progressions. We argue that, at least in certain ranges, these estimates agree with a conjecture by H. L. Montgomery.

Cited by

• The minimal periodicity for integral bases of pure number fields

Related

• On Bourgain's bound for short exponential sums and squarefree numbers
• Moments of moments of primes in arithmetic progressions
• Primes in arithmetic progressions on average II
• On the distribution of r-tuples of squarefree numbers in short intervals
• On two conjectures concerning squarefree numbers in arithmetic\n progressions