Variance of Squarefull Numbers in Short Intervals

2022/05/24 by Tsz Ho Chan, Chan, Tsz Ho
Mathematics · #Analytic Number Theory Research #FOS: Mathematics #Meromorphic and Entire Functions #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2205.12108

openalex publication_date 2022/05/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we study the variance of the number of squarefull numbers in short intervals. As a result, we are able to prove that, for any 0 < θ< 1/2, almost all short intervals (x, x + x^{1/2 + θ}] contain about (ζ(3/2))/(2 ζ(3)) x^θ squarefull numbers.

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