On the distribution of squarefree integers in arithmetic progressions

2014/11/10 by Pierre Le Boudec, Boudec, Pierre Le · 1 citation
Mathematics · #11N37 #11N69 #Analytic Number Theory Research #FOS: Mathematics #Limits and Structures in Graph Theory #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.1411.2360

openalex publication_date 2014/11/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the error term of the asymptotic formula for the number of squarefree integers up to some bound, and lying in some arithmetic progression a (mod q). In particular, we prove an upper bound for its variance as a varies over (ℤ/qℤ)^× which considerably improves upon earlier work of Blomer.

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• On two conjectures concerning squarefree numbers in arithmetic\n progressions

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